Deck 9: Exponential and Logarithmic Functions

Full screen (f)
exit full mode
Question
Identify the horizontal asymptote of g(x)=(78)x+7g ( x ) = \left( \frac { 7 } { 8 } \right) ^ { x } + 7 .

A) y=778y = 7 \frac { 7 } { 8 }
B)x -axis
C) y=-7
D) y=7
E) y=78y = - \frac { 7 } { 8 }
Use Space or
up arrow
down arrow
to flip the card.
Question
Match f(x)=4x1f ( x ) = 4 ^ { x } - 1 with its graph.

A)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Identify the horizontal asymptote of g(x)=4x+2g ( x ) = 4 ^ { x + 2 } .

A)x -axis
B) y=2
C) y=-2
D) y=16
E) y=-16
Question
Sketch the graph of the function f(x)=8xf ( x ) = 8 ^ { - x } .

A)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Evaluate the function as indicated. Round to three decimal places if necessary. 10,000(1.01)3tt=3\begin{array} { c } 10,000 ( 1.01 ) ^ { 3 t } \\t = 3\end{array}

A)10,303.010
B)10,936.853
C)91,999.387
D)4702.847
E)90,900.000
Question
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.7xx=1\begin{aligned}G ( x ) & = 1.7 ^ { - x } \\x & = - 1\end{aligned}

A)-0.588
B)0.588
C)2.700
D)1.700
E)-1.700
Question
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.5xx=1\begin{aligned}G ( x ) & = 1.5 ^ { - x } \\x & = 1\end{aligned}

A)0.500
B)0.667
C)2.500
D)-0.667
E)-1.500
Question
Match f(x)=3xf ( x ) = - 3 ^ { x } with its graph.

A)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
ex+6ex\frac { e ^ { x + 6 } } { e ^ { x } }

A) 1+e6x1 + e ^ { 6 - x }
B) e6e ^ { 6 }
C) e1+6xe^{1 + \frac { 6 } { x }}
D) 1+e6x1 + e ^ { \frac { 6 } { x } }
E)cannot be simplified
Question
Evaluate the expression 626 ^ { \sqrt { 2 } } . Round your answer to three decimal places.

A)8.485
B)3.000
C)12.603
D)2.449
E)22.274
Question
Simplify the expression. (4ex)3\left( 4 e ^ { x } \right) ^ { 3 }

A) 64e3x64 e ^ { 3 x }
B) 4e3x4 e ^ { 3 x }
C) 4ex34 e ^ { x ^ { 3 } }
D) 12e3x12 e ^ { 3 x }
E) 64ex364 e ^ { x ^ { 3 } }
Question
Simplify the expression. 5e6x- 5 e ^ { - 6 x }

A) 5e6x5 e ^ { 6 x }
B) 5e6x- \frac { 5 } { e ^ { 6 x } }
C) 5e6x- 5 \sqrt [ 6 x ] { e }
D) 5e6x\frac { 5 } { e ^ { 6 x } }
E) 5e6x\sqrt [ 6 x ] { - 5 e }
Question
Simplify the expression. 8x8x18 ^ { x } \cdot 8 ^ { x - 1 }

A) 82x18 ^ { 2 x - 1 }
B) 64x2x64 ^ { x ^ { 2 } - x }
C) 18\frac { 1 } { 8 }
D) 8x8 ^ { x }
E) 8x2x8 ^ { x ^ { 2 } - x }
Question
Evaluate the function as indicated. Round to three decimal places if necessary.
10,000(1.07)4tt=1\begin{array}{ c}10,000 ( 1.07 ) ^ { 4 t } \\ t = 1\end{array}

A)13,107.960
B)1310.796
C)10,700.000
D)42,800.000
E)44,076.205
Question
Evaluate the function as indicated. Round to three decimal places if necessary.

10,000(1.09)3tt=5.5\begin{array}{c} 10,000 ( 1.09 ) ^ { 3 t }\\t = 5.5\end{array}

A)212,352.559
B)227981.657
C)16,063.706
D)41,451.210
E)179,850.000
Question
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=50e0.1xx=20\begin{aligned}g ( x ) & = 50 e ^ { - 0.1 x } \\x & = - 20\end{aligned}

A)-6.767
B)6.767
C)-904.837
D)369.453
E)210.588
Question
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=100e0.5xx=8\begin{aligned}g ( x ) & = 100 e ^ { - 0.5 x } \\x & = 8\end{aligned}

A)-1087.313
B)1.832
C)5459.815
D)1.593
E)-485.225
Question
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=70e0.5xx=4\begin{aligned}g ( x ) & = 70 e ^ { - 0.5 x } \\x & = 4\end{aligned}

A)-9.473
B)10.705
C)-169.829
D)9.473
E)517.234
Question
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.7xx=3\begin{aligned}G ( x ) & = 1.7 ^ { - x } \\x & = \sqrt { 3 }\end{aligned}

A)0.399
B)-2.944
C)-0.032
D)2.507
E)not a real number
Question
Identify the horizontal asymptote of h(x)=12(15x)h ( x ) = \frac { 1 } { 2 } \left( 15 ^ { - x } \right) .

A) y=12y = \frac { 1 } { 2 }
B) y=130y = \frac { 1 } { 30 }
C) y=115y = \frac { 1 } { 15 }
D) y=15
E)x -axis
Question
After t years, the remaining mass y (in grams)of 24 grams of a radioactive elements whose half-life is 30 years is given by y=24(12)t/30,t0y = 24 \left( \frac { 1 } { 2 } \right) ^ { t / 30 } , t \geq 0 . How much of the initial mass remains after 50 years? Round your answers to two decimal places.

A)7.56 grams
B)14.40 grams
C)3.17 grams
D)16.44 grams
E)nothing remains
Question
The population P (in millions)of the United States from 1970 to 2000 can be approximated by the exponential function P(t)=203.0(1.0107)tP ( t ) = 203.0 ( 1.0107 ) ^ { t } , where t is the time in years with t=0t = 0 corresponding to 1970. Use the model to estimate the population in the year 2,005. Round your answer to one decimal place. Source: U.S. Census Bureau

A)205.2 million
B)7,181.0 million
C)223.9million
D)294.6 million
E)1.5 million
Question
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x+5f ( x ) = 4 x + 5 and g(x)=x2g ( x ) = x - 2 .

A) 4x+34 x + 3
B) 4x23x104 x ^ { 2 } - 3 x - 10
C) 4x34 x - 3
D) 5x+35 x + 3
E) 4x28x+54 x ^ { 2 } - 8 x + 5
Question
Determine the principal P (to the nearest cent)that will yield a balance of <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded once per year. Round the answer to two decimal places.</strong> A)$56,306.31 B)$568,181.82 C)$68,460.62 D)$55,625.00 E)$38,461.03 <div style=padding-top: 35px> dollars when invested at rate <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded once per year. Round the answer to two decimal places.</strong> A)$56,306.31 B)$568,181.82 C)$68,460.62 D)$55,625.00 E)$38,461.03 <div style=padding-top: 35px> for 40 years, compounded once per year. Round the answer to two decimal places.

A)$56,306.31
B)$568,181.82
C)$68,460.62
D)$55,625.00
E)$38,461.03
Question
The value of a piece of property doubles every 16 years. You buy the property for $50,000. Its value t years after the date of purchase should be V(t)=50,000(2)t/16V ( t ) = 50,000 ( 2 ) ^ { t / 16 } . Use the model to approximate (to the nearest thousand dollars)the value of the property after 4 years.

A)$50,000
B)$6,400,000
C)$75,000
D)$59,000
E)$100,000
Question
Determine the principal P (to the nearest cent)that will yield a balance of A=500,000A = 500,000 dollars when invested at rate r=8.5%r = 8.5 \% for 40 years, compounded continuously. Round the answer to two decimal places.

A)$611,887.72
B)$495,364.63
C)$16,686.63
D)$13,015.58
E)$13,608.96
Question
Determine the principal P (to the nearest cent)that will yield a balance of A=500,000A = 500,000 dollars when invested at rate r=6.5%r = 6.5 \% for 40 years, compounded 12 times per year. Round the answer to two decimal places.

A)$973.96
B)$273,927.55
C)$16,025.64
D)$37,398.27
E)$402,834.63
Question
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 <div style=padding-top: 35px> dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 <div style=padding-top: 35px> for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 <div style=padding-top: 35px> , compounded 365 times per year. Round the answer to two decimal places.

A)$9,855.00
B)$8,042.90
C)$7,378.81
D)$6,027.12
E)$7,377.99
Question
Find (fg)(4)( f \circ g ) ( 4 ) where f(x)=5x+9f ( x ) = 5 x + 9 and g(x)=x5g ( x ) = x - 5 .

A)24
B)-29
C)4
D)28
E)-11
Question
Identify the transformation of f(x)=2xf ^ { \prime } ( x ) = 2 ^ { x } . h(x)=2x6h ( x ) = 2 ^ { x - 6 }

A)a shift of 6 units downward
B)a shift of 6 units to the left
C)a reflection about the line x=6
D)a shift of 6 units to the right
E)a shift of 6 units upward
Question
Find (gf)(3)( g \circ f ) ( 3 ) where f(x)=5x+2f ( x ) = 5 x + 2 and g(x)=x5g ( x ) = x - 5 .

A)12
B)15
C)-28
D)-8
E)-34
Question
Find (fg)(x)( f \circ g ) ( x ) where f(x)=6x+9f ( x ) = 6 x + 9 and g(x)=x7g ( x ) = x - 7 .

A) 6x+26 x + 2
B) 6x336 x - 33
C) 6x233x636 x ^ { 2 } - 33 x - 63
D) 6x242x+96 x ^ { 2 } - 42 x + 9
E) 7x+337 x + 33
Question
Determine the principal P (to the nearest cent)that will yield a balance of A=2,500,000A = 2,500,000 dollars when invested at rate r=10%r = 10 \% for 40 years, compounded 365 times per year. Round the answer to two decimal places.

A)$38,920.73
B)$1,541,095.89
C)$1,712.33
D)$2,472,756.03
E)$45,814.19
Question
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 <div style=padding-top: 35px> dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 <div style=padding-top: 35px> for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 <div style=padding-top: 35px> , compounded continuously. Round the answer to two decimal places.

A)$8,154.85
B)$10,950.00
C)$8,153.73
D)$8,887.56
E)$6,030.15
Question
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 <div style=padding-top: 35px> dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 <div style=padding-top: 35px> for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 <div style=padding-top: 35px> , compounded one time per year. Round the answer to two decimal places.

A)$33,000.00
B)$4,781.23
C)$3,000.00
D)$6,000.00
E)$7,781.23
Question
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 <div style=padding-top: 35px> dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 <div style=padding-top: 35px> for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 <div style=padding-top: 35px> , compounded 12 times per year. Round the answer to two decimal places.

A)$529.94
B)$4,700.00
C)$1,126.10
D)$1,004.83
E)$6,359.33
Question
Find (fg)(x)( f \circ g ) ( x ) where f(x)=2x+6f ( x ) = 2 x + 6 and g(x)=x22g ( x ) = x ^ { 2 } - 2 .

A) 2x312x24x122 x ^ { 3 } 12 x ^ { 2 } - 4 x - 12
B) 2x2+22 x ^ { 2 } + 2
C) 4x2+24x+344 x ^ { 2 } + 24 x + 34
D) 4x2+44 x ^ { 2 } + 4
E) 2x2+42 x ^ { 2 } + 4
Question
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 <div style=padding-top: 35px> dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 <div style=padding-top: 35px> for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 <div style=padding-top: 35px> , compounded 4 times per year. Round the answer to two decimal places.

A)$3,161.40
B)$12,000.00
C)$12,645.59
D)$94,298.50
E)$6,392.88
Question
Identify the transformation of f(x)=15xf ( x ) = 15 ^ { x } . h(x)=15xh ( x ) = - 15 ^ { x }

A)a reflection about the y -axis
B)a reflection about the x -axis
C)a reflection about the line y=-x
D)a reflection about the line y=x
E)a reflection about the line x=15
Question
Determine the principal P (to the nearest cent)that will yield a balance of <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded 4 times per year. Round the answer to two decimal places.</strong> A)$173,611.11 B)$14,218.75 C)$1,026,614.38 D)$147,569.44 E)$71,090.14 <div style=padding-top: 35px> dollars when invested at rate <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded 4 times per year. Round the answer to two decimal places.</strong> A)$173,611.11 B)$14,218.75 C)$1,026,614.38 D)$147,569.44 E)$71,090.14 <div style=padding-top: 35px> for 40 years, compounded 4 times per year. Round the answer to two decimal places.

A)$173,611.11
B)$14,218.75
C)$1,026,614.38
D)$147,569.44
E)$71,090.14
Question
Use the function of f(x)={(2,3),(1,1),(0,0),(1,1),(2,3)}f ( x ) = \{ ( - 2,3 ) , ( - 1,1 ) , ( 0,0 ) , ( 1 , - 1 ) , ( 2 , - 3 ) \} and g(x)={(3,2),(1,3),(0,3),(2,4),(3,4)}g ( x ) = \{ ( - 3 , - 2 ) , ( - 1 , - 3 ) , ( 0,3 ) , ( 2,4 ) , ( 3,4 ) \} to find the value of (gf)(2)( g \circ f ) ( - 2 ) .

A)4
B)3
C)-3
D)2
E)-2
Question
Find the inverse function of f(x)=6xf ( x ) = 6 - x .

A) f1(x)=6xf ^ { - 1 } ( x ) = 6 - x
B) f1(x)=6xf ^ { - 1 } ( x ) = - 6 - x
C) f1(x)=6f ^ { - 1 } ( x ) = 6
D) f1(x)=6+xf ^ { - 1 } ( x ) = 6 + x
E) f1(x)=6+xf ^ { - 1 } ( x ) = - 6 + x
Question
Find the inverse function of f(x)=47xf ( x ) = 4 - 7 x .

A) f1(x)=17x4f ^ { - 1 } ( x ) = \frac { 1 } { 7 } x - 4
B) f1(x)=4x7f ^ { - 1 } ( x ) = \frac { 4 - x } { 7 }
C) f1(x)=17x+4f ^ { - 1 } ( x ) = \frac { 1 } { 7 } x + 4
D) f1(x)=x47f ^ { - 1 } ( x ) = \frac { x - 4 } { 7 }
E)The function does not have an inverse.
Question
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.
 <strong>Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.    f ( x ) = \sqrt { 81 - x ^ { 2 } } </strong> A)f is one-to-one B)f is not one-to-one C)cannot be determined <div style=padding-top: 35px>
f(x)=81x2f ( x ) = \sqrt { 81 - x ^ { 2 } }

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined
Question
Which statement(s)verify that f(x)=4x+1f ( x ) = \frac { 4 } { x + 1 } and g(x)=4xxg ( x ) = \frac { 4 - x } { x } are inverse?

A) f(x)+g(x)=4x+1+4xx=0f ( x ) + g ( x ) = \frac { 4 } { x + 1 } + \frac { 4 - x } { x } = 0
B) f(x)g(x)=4x+14xx=1\frac { f ( x ) } { g ( x ) } = \frac { \frac { 4 } { x + 1 } } { \frac { 4 - x } { x } } = 1
C) f(g(x))=44xx+1=x,g(f(x))=44x+14x+1=xf ( g ( x ) ) = \frac { 4 } { \frac { 4 - x } { x } + 1 } = x , g ( f ( x ) ) = \frac { 4 - \frac { 4 } { x + 1 } } { \frac { 4 } { x + 1 } } = x
D) f(x)+g(x)=4x+1+4xx=1f ( x ) + g ( x ) = \frac { 4 } { x + 1 } + \frac { 4 - x } { x } = 1
E) f(g(x))=44xx+1=1;g(f(x))=4x+14x+1=1f ( g ( x ) ) = \frac { 4 } { \frac { 4 - x } { x } + 1 } = 1 ; g ( f ( x ) ) = \frac { \frac { 4 } { x + 1 } } { \frac { 4 } { x + 1 } } = 1
Question
Find the domain of gfg \circ f where f(x)=xx5f ( x ) = \frac { x } { x - 5 } and g(x)=xg ( x ) = \sqrt { x } .

A) [0,5)(5,)[ 0,5 ) \cup ( 5 , \infty )
B) (25,)( 25 , \infty )
C) (,0](5,)( - \infty , 0 ] \cup ( 5 , \infty )
D) [0,25)(25,)[ 0,25 ) \cup ( 25 , \infty )
E) (,25)(25,)( - \infty , 25 ) \cup ( 25 , \infty )
Question
Find the domain of gfg \circ f where f(x)=x2f ( x ) = \sqrt { x - 2 } and g(x)=x+6g ( x ) = x + 6 .

A) [2,)[ 2 , \infty )
B) [4,)[ 4 , \infty )
C) [4,)[ - 4 , \infty )
D) [6,)[ - 6 , \infty )
E) [0,)[ 0 , \infty )
Question
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.
 <strong>Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.    f ( x ) = 5 \sqrt { - x } </strong> A)f is one-to-one B)f is not one-to-one C)cannot be determined <div style=padding-top: 35px>
f(x)=5xf ( x ) = 5 \sqrt { - x }

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined
Question
Which statement(s)verify that f(x)=9x1f ( x ) = 9 x - 1 and g(x)=19(x+1)g ( x ) = \frac { 1 } { 9 } ( x + 1 ) are inverse?

A) f(x)g(x)=(9x1)19(x+1)=1f ( x ) \cdot g ( x ) = ( 9 x - 1 ) \frac { 1 } { 9 } ( x + 1 ) = - 1
B) f(g(x))=(9(19x)+1)1=x,g(f(x))=19(9(x1)+1)=xf ( g ( x ) ) = \left( 9 \left( \frac { 1 } { 9 } x \right) + 1 \right) - 1 = x , g ( f ( x ) ) = \frac { 1 } { 9 } ( 9 ( x - 1 ) + 1 ) = x
C) f(g(x))=(9(19x)+1)1=x;g(f(x))=19((9x1)+1)=xf ( g ( x ) ) = \left( 9 \left( \frac { 1 } { 9 } x \right) + 1 \right) - 1 = x ; g ( f ( x ) ) = \frac { 1 } { 9 } ( ( 9 x - 1 ) + 1 ) = x
D) f(g(x))=9(19(x+1))1=x;g(f(x))=19((9x1)+1)=xf ( g ( x ) ) = 9 \left( \frac { 1 } { 9 } ( x + 1 ) \right) - 1 = x ; g ( f ( x ) ) = \frac { 1 } { 9 } ( ( 9 x - 1 ) + 1 ) = x
E) f(x)g(x)=9(x1)9(x+1)=1\frac { f ( x ) } { g ( x ) } = \frac { 9 ( x - 1 ) } { 9 ( x + 1 ) } = - 1
Question
Find (gf)(5)( g \circ f ) ( - 5 ) where f(x)=3x+4f ( x ) = 3 x + 4 and g(x)=x26g ( x ) = x ^ { 2 } - 6 .

A)73
B)115
C)223
D)61
E)-9
Question
Find the domain of gfg \circ f where f(x)=xx64f ( x ) = \frac { x } { x - 64 } and g(x)=xg ( x ) = \sqrt { x } .

A) (0,64](64,)( 0,64 ] \cup ( 64 , \infty )
B) (,0](64,)( - \infty , 0 ] \cup ( 64 , \infty )
C) [0,8)(8,)[ 0,8 ) \cup ( 8 , \infty )
D) (0,)( 0 , \infty )
E) (0,)( 0 , \infty ) .
Question
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x+7f ( x ) = 4 x + 7 and g(x)=x21g ( x ) = x ^ { 2 } - 1 .

A) 4x328x24x74 x ^ { 3 } 28 x ^ { 2 } - 4 x - 7
B) 4x2+34 x ^ { 2 } + 3
C) 16x2+56x+4816 x ^ { 2 } + 56 x + 48
D) 16x2+616 x ^ { 2 } + 6
E) 4x2+64 x ^ { 2 } + 6
Question
Find the inverse function of f(t)=t75f ( t ) = t ^ { 7 } - 5 .

A) f1(t)=t57f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t - 5 }
B) f1(t)=t75f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t } - 5
C) f1(t)=t+57f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t + 5 }
D) f1(t)=t7+5f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t } + 5
E)The function does not have an inverse.
Question
Find the domain of fgf \circ g where f(x)=x7f ( x ) = \sqrt { x - 7 } and g(x)=x+5g ( x ) = x + 5 .

A) [5,)[ - 5 , \infty )
B) [0,)[ 0 , \infty )
C) [7,)[ 7 , \infty )
D) [2,)[ - 2 , \infty )
E) [2,)[ 2 , \infty )
Question
Find (gf)(3)( g \circ f ) ( 3 ) where f(x)=2x11f ( x ) = 2 x - 11 and g(x)=x+6g ( x ) = \sqrt { x + 6 } .

A)-16
B)2
C)1
D)-15
E)-5
Question
Find (fg)(3)( f \circ g ) ( 3 ) where f(x)=2x38f ( x ) = 2 x - 38 and g(x)=x+33g ( x ) = \sqrt { x + 33 } .

A)-64
B)-26
C)-5
D)-192
E)1
Question
Which statement(s)verify that f(x)=x+47f ( x ) = \sqrt [ 7 ] { x + 4 } and g(x)=x24g ( x ) = x ^ { 2 } - 4 are inverse?

A) f(g(x))=x74+47=x;g(f(x))=(x7)7+44=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } - 4 + 4 } = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x } ) ^ { 7 } + 4 - 4 = x
B) f(x)g(x)=x+47(x74)=xf ( x ) \cdot g ( x ) = \sqrt [ 7 ] { x + 4 } \cdot \left( x ^ { 7 } - 4 \right) = x
C) f(g(x))=x774+4=x;g(f(x))=(x+47)74=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } } - 4 + 4 = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x + 4 } ) ^ { 7 } - 4 = x
D) f(g(x))=x74+47=x;g(f(x))=(x+47)74=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } - 4 + 4 } = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x + 4 } ) ^ { 7 } - 4 = x
E) f(x)g(x)=x+47x7b=1\frac { f ( x ) } { g ( x ) } = \frac { \sqrt [ 7 ] { x + 4 } } { x ^ { 7 } - b } = - 1
Question
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x8f ( x ) = 4 x - 8 and g(x)=x+4g ( x ) = \sqrt { x + 4 } .

A) 4x44 \sqrt { x - 4 }
B) 4x4\sqrt { 4 x - 4 }
C) 4x+168\sqrt { 4 x + 16 } - 8
D) (4x8)x+4( 4 x - 8 ) \sqrt { x + 4 }
E) 4x+484 \sqrt { x + 4 } - 8
Question
Find (fg)(x)( f \circ g ) ( x ) where f(x)=4x3f ( x ) = 4 x - 3 and g(x)=x+8g ( x ) = \sqrt { x + 8 } .

A) 4x+834 \sqrt { x + 8 } - 3
B) 4x+5\sqrt { 4 x + 5 }
C) 4x+323\sqrt { 4 x + 32 } - 3
D) 4x+54 \sqrt { x + 5 }
E) (4x3)x+8( 4 x - 3 ) \sqrt { x + 8 }
Question
Find (fg)(3)( f \circ g ) ( - 3 ) where f(x)=4x+6f ( x ) = 4 x + 6 and g(x)=x24g ( x ) = x ^ { 2 } - 4 .

A)32
B)38
C)146
D)132
E)26
Question
Match f(x)=log2(x+3)f ( x ) = \log _ { 2 } ( x + 3 ) with its graph.

A)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Match f(x)=log4(x)f ( x ) = \log _ { 4 } ( - x ) with its graph.

A)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Write the exponential equation 7292/3=81729 ^ { 2 / 3 } = 81 in logarithmic form.

A) log72981=23\log _ { 729 } 81 = \frac { 2 } { 3 }
B) log9729=9\log _ { 9 } 729 = 9
C) log981=2\log _ { 9 } 81 = 2
D) log72981=32\log _ { 729 } 81 = \frac { 3 } { 2 }
E) log72981=3\log _ { 729 } 81 = 3
Question
Identify the vertical asymptote of g(t)=log5tg ( t ) = - \log _ { 5 } t .

A) t=5
B) t=15t = - \frac { 1 } { 5 }
C) t=15t = \frac { 1 } { 5 }
D) t=-5
E)y -axis
Question
Evaluate the logarithm. log6416\log _ { 64 } 16

A) 12\frac { 1 } { 2 }
B) 3
C) 2
D) 23\frac { 2 } { 3 }
E) log6416\log _ { 64 } 16 is undefined.
Question
Use a calculator to evaluate the common logarithm log1047\log _ { 10 } 47 . Round your answer to four decimal places.

A)1.6812
B)1.6721
C)3.8501
D)1.9777
E)3.8712
Question
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Find the inverse function of f(x)=x+5,x5f ( x ) = \sqrt { x + 5 } , x \geq - 5 .

A) f1(x)=x25,x0f ^ { - 1 } ( x ) = x ^ { 2 } - 5 , x \geq 0
B) f1(x)=x225,x0f ^ { - 1 } ( x ) = x ^ { 2 } - 25 , x \geq 0
C) f1(x)=(x25)2f ^ { - 1 } ( x ) = ( x - 25 ) ^ { 2 }
D) f1(x)=(x5)2f ^ { - 1 } ( x ) = ( x - 5 ) ^ { 2 }
E)The function does not have an inverse.
Question
Evaluate the logarithm. log9(0)\log _ { 9 } ( 0 )

A) 19\frac { 1 } { 9 }
B)1
C) -1
D)0
E)Undefined
Question
Identify the vertical asymptote of g(t)=6+log7tg ( t ) = - 6 + \log _ { 7 } t .

A) t=-6
B) t=6
C) t=7
D) t=-7
E)y -axis
Question
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Evaluate the logarithm. log36216\log _ { 36 } 216

A) 32\frac { 3 } { 2 }
B)3
C) 23\frac { 2 } { 3 }
D)6
E) log36216\log _ { 36 } 216 is undefined.
Question
Match f(x)=3+log5xf ( x ) = 3 + \log _ { 5 } x with its graph.

A)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Match f(x)=log2xf ( x ) = - \log _ { 2 } x with its graph.

A)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Evaluate the logarithm. log3[27]\log _ { 3 } [ 27 ]

A) -3
B)9
C) log327\log _ { 3 } 27
D)3
E) log327\log _ { 3 } 27 is undefined.
Question
Evaluate the logarithm. log6(6)\log _ { 6 } ( - 6 )

A)0
B) 16\frac { 1 } { 6 }
C) -1
D) e1e^ { - 1 }
E) log6(6)\log _ { 6 } ( - 6 ) is undefined.
Question
Write the logarithmic equation log2132=5\log _ { 2 } \frac { 1 } { 32 } = - 5 in exponential form.

A) 25=1322 ^ { - 5 } = \frac { 1 } { 32 }
B) 25=1322 ^ { - 5 } = - \frac { 1 } { 32 }
C) 52=1105 ^ { 2 } = \frac { 1 } { 10 }
D) 52=325 ^ { 2 } = 32
E) 25=152 ^ { - 5 } = \frac { 1 } { 5 }
Question
Evaluate the logarithm. log51125\log _ { 5 } \frac { 1 } { 125 }

A) 3\sqrt { 3 }
B) -3
C)0
D) 13\frac { 1 } { 3 }
E) log51125\log _ { 5 } \frac { 1 } { 125 } is undefined.
Question
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Unlock Deck
Sign up to unlock the cards in this deck!
Unlock Deck
Unlock Deck
1/165
auto play flashcards
Play
simple tutorial
Full screen (f)
exit full mode
Deck 9: Exponential and Logarithmic Functions
1
Identify the horizontal asymptote of g(x)=(78)x+7g ( x ) = \left( \frac { 7 } { 8 } \right) ^ { x } + 7 .

A) y=778y = 7 \frac { 7 } { 8 }
B)x -axis
C) y=-7
D) y=7
E) y=78y = - \frac { 7 } { 8 }
y=7
2
Match f(x)=4x1f ( x ) = 4 ^ { x } - 1 with its graph.

A)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)

3
Identify the horizontal asymptote of g(x)=4x+2g ( x ) = 4 ^ { x + 2 } .

A)x -axis
B) y=2
C) y=-2
D) y=16
E) y=-16
x -axis
4
Sketch the graph of the function f(x)=8xf ( x ) = 8 ^ { - x } .

A)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)
B)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)
C)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)
D)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)
E)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
5
Evaluate the function as indicated. Round to three decimal places if necessary. 10,000(1.01)3tt=3\begin{array} { c } 10,000 ( 1.01 ) ^ { 3 t } \\t = 3\end{array}

A)10,303.010
B)10,936.853
C)91,999.387
D)4702.847
E)90,900.000
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
6
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.7xx=1\begin{aligned}G ( x ) & = 1.7 ^ { - x } \\x & = - 1\end{aligned}

A)-0.588
B)0.588
C)2.700
D)1.700
E)-1.700
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
7
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.5xx=1\begin{aligned}G ( x ) & = 1.5 ^ { - x } \\x & = 1\end{aligned}

A)0.500
B)0.667
C)2.500
D)-0.667
E)-1.500
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
8
Match f(x)=3xf ( x ) = - 3 ^ { x } with its graph.

A)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
9
ex+6ex\frac { e ^ { x + 6 } } { e ^ { x } }

A) 1+e6x1 + e ^ { 6 - x }
B) e6e ^ { 6 }
C) e1+6xe^{1 + \frac { 6 } { x }}
D) 1+e6x1 + e ^ { \frac { 6 } { x } }
E)cannot be simplified
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
10
Evaluate the expression 626 ^ { \sqrt { 2 } } . Round your answer to three decimal places.

A)8.485
B)3.000
C)12.603
D)2.449
E)22.274
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
11
Simplify the expression. (4ex)3\left( 4 e ^ { x } \right) ^ { 3 }

A) 64e3x64 e ^ { 3 x }
B) 4e3x4 e ^ { 3 x }
C) 4ex34 e ^ { x ^ { 3 } }
D) 12e3x12 e ^ { 3 x }
E) 64ex364 e ^ { x ^ { 3 } }
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
12
Simplify the expression. 5e6x- 5 e ^ { - 6 x }

A) 5e6x5 e ^ { 6 x }
B) 5e6x- \frac { 5 } { e ^ { 6 x } }
C) 5e6x- 5 \sqrt [ 6 x ] { e }
D) 5e6x\frac { 5 } { e ^ { 6 x } }
E) 5e6x\sqrt [ 6 x ] { - 5 e }
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
13
Simplify the expression. 8x8x18 ^ { x } \cdot 8 ^ { x - 1 }

A) 82x18 ^ { 2 x - 1 }
B) 64x2x64 ^ { x ^ { 2 } - x }
C) 18\frac { 1 } { 8 }
D) 8x8 ^ { x }
E) 8x2x8 ^ { x ^ { 2 } - x }
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
14
Evaluate the function as indicated. Round to three decimal places if necessary.
10,000(1.07)4tt=1\begin{array}{ c}10,000 ( 1.07 ) ^ { 4 t } \\ t = 1\end{array}

A)13,107.960
B)1310.796
C)10,700.000
D)42,800.000
E)44,076.205
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
15
Evaluate the function as indicated. Round to three decimal places if necessary.

10,000(1.09)3tt=5.5\begin{array}{c} 10,000 ( 1.09 ) ^ { 3 t }\\t = 5.5\end{array}

A)212,352.559
B)227981.657
C)16,063.706
D)41,451.210
E)179,850.000
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
16
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=50e0.1xx=20\begin{aligned}g ( x ) & = 50 e ^ { - 0.1 x } \\x & = - 20\end{aligned}

A)-6.767
B)6.767
C)-904.837
D)369.453
E)210.588
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
17
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=100e0.5xx=8\begin{aligned}g ( x ) & = 100 e ^ { - 0.5 x } \\x & = 8\end{aligned}

A)-1087.313
B)1.832
C)5459.815
D)1.593
E)-485.225
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
18
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=70e0.5xx=4\begin{aligned}g ( x ) & = 70 e ^ { - 0.5 x } \\x & = 4\end{aligned}

A)-9.473
B)10.705
C)-169.829
D)9.473
E)517.234
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
19
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.7xx=3\begin{aligned}G ( x ) & = 1.7 ^ { - x } \\x & = \sqrt { 3 }\end{aligned}

A)0.399
B)-2.944
C)-0.032
D)2.507
E)not a real number
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
20
Identify the horizontal asymptote of h(x)=12(15x)h ( x ) = \frac { 1 } { 2 } \left( 15 ^ { - x } \right) .

A) y=12y = \frac { 1 } { 2 }
B) y=130y = \frac { 1 } { 30 }
C) y=115y = \frac { 1 } { 15 }
D) y=15
E)x -axis
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
21
After t years, the remaining mass y (in grams)of 24 grams of a radioactive elements whose half-life is 30 years is given by y=24(12)t/30,t0y = 24 \left( \frac { 1 } { 2 } \right) ^ { t / 30 } , t \geq 0 . How much of the initial mass remains after 50 years? Round your answers to two decimal places.

A)7.56 grams
B)14.40 grams
C)3.17 grams
D)16.44 grams
E)nothing remains
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
22
The population P (in millions)of the United States from 1970 to 2000 can be approximated by the exponential function P(t)=203.0(1.0107)tP ( t ) = 203.0 ( 1.0107 ) ^ { t } , where t is the time in years with t=0t = 0 corresponding to 1970. Use the model to estimate the population in the year 2,005. Round your answer to one decimal place. Source: U.S. Census Bureau

A)205.2 million
B)7,181.0 million
C)223.9million
D)294.6 million
E)1.5 million
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
23
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x+5f ( x ) = 4 x + 5 and g(x)=x2g ( x ) = x - 2 .

A) 4x+34 x + 3
B) 4x23x104 x ^ { 2 } - 3 x - 10
C) 4x34 x - 3
D) 5x+35 x + 3
E) 4x28x+54 x ^ { 2 } - 8 x + 5
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
24
Determine the principal P (to the nearest cent)that will yield a balance of <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded once per year. Round the answer to two decimal places.</strong> A)$56,306.31 B)$568,181.82 C)$68,460.62 D)$55,625.00 E)$38,461.03 dollars when invested at rate <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded once per year. Round the answer to two decimal places.</strong> A)$56,306.31 B)$568,181.82 C)$68,460.62 D)$55,625.00 E)$38,461.03 for 40 years, compounded once per year. Round the answer to two decimal places.

A)$56,306.31
B)$568,181.82
C)$68,460.62
D)$55,625.00
E)$38,461.03
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
25
The value of a piece of property doubles every 16 years. You buy the property for $50,000. Its value t years after the date of purchase should be V(t)=50,000(2)t/16V ( t ) = 50,000 ( 2 ) ^ { t / 16 } . Use the model to approximate (to the nearest thousand dollars)the value of the property after 4 years.

A)$50,000
B)$6,400,000
C)$75,000
D)$59,000
E)$100,000
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
26
Determine the principal P (to the nearest cent)that will yield a balance of A=500,000A = 500,000 dollars when invested at rate r=8.5%r = 8.5 \% for 40 years, compounded continuously. Round the answer to two decimal places.

A)$611,887.72
B)$495,364.63
C)$16,686.63
D)$13,015.58
E)$13,608.96
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
27
Determine the principal P (to the nearest cent)that will yield a balance of A=500,000A = 500,000 dollars when invested at rate r=6.5%r = 6.5 \% for 40 years, compounded 12 times per year. Round the answer to two decimal places.

A)$973.96
B)$273,927.55
C)$16,025.64
D)$37,398.27
E)$402,834.63
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
28
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 , compounded 365 times per year. Round the answer to two decimal places.

A)$9,855.00
B)$8,042.90
C)$7,378.81
D)$6,027.12
E)$7,377.99
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
29
Find (fg)(4)( f \circ g ) ( 4 ) where f(x)=5x+9f ( x ) = 5 x + 9 and g(x)=x5g ( x ) = x - 5 .

A)24
B)-29
C)4
D)28
E)-11
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
30
Identify the transformation of f(x)=2xf ^ { \prime } ( x ) = 2 ^ { x } . h(x)=2x6h ( x ) = 2 ^ { x - 6 }

A)a shift of 6 units downward
B)a shift of 6 units to the left
C)a reflection about the line x=6
D)a shift of 6 units to the right
E)a shift of 6 units upward
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
31
Find (gf)(3)( g \circ f ) ( 3 ) where f(x)=5x+2f ( x ) = 5 x + 2 and g(x)=x5g ( x ) = x - 5 .

A)12
B)15
C)-28
D)-8
E)-34
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
32
Find (fg)(x)( f \circ g ) ( x ) where f(x)=6x+9f ( x ) = 6 x + 9 and g(x)=x7g ( x ) = x - 7 .

A) 6x+26 x + 2
B) 6x336 x - 33
C) 6x233x636 x ^ { 2 } - 33 x - 63
D) 6x242x+96 x ^ { 2 } - 42 x + 9
E) 7x+337 x + 33
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
33
Determine the principal P (to the nearest cent)that will yield a balance of A=2,500,000A = 2,500,000 dollars when invested at rate r=10%r = 10 \% for 40 years, compounded 365 times per year. Round the answer to two decimal places.

A)$38,920.73
B)$1,541,095.89
C)$1,712.33
D)$2,472,756.03
E)$45,814.19
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
34
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 , compounded continuously. Round the answer to two decimal places.

A)$8,154.85
B)$10,950.00
C)$8,153.73
D)$8,887.56
E)$6,030.15
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
35
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 , compounded one time per year. Round the answer to two decimal places.

A)$33,000.00
B)$4,781.23
C)$3,000.00
D)$6,000.00
E)$7,781.23
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
36
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 , compounded 12 times per year. Round the answer to two decimal places.

A)$529.94
B)$4,700.00
C)$1,126.10
D)$1,004.83
E)$6,359.33
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
37
Find (fg)(x)( f \circ g ) ( x ) where f(x)=2x+6f ( x ) = 2 x + 6 and g(x)=x22g ( x ) = x ^ { 2 } - 2 .

A) 2x312x24x122 x ^ { 3 } 12 x ^ { 2 } - 4 x - 12
B) 2x2+22 x ^ { 2 } + 2
C) 4x2+24x+344 x ^ { 2 } + 24 x + 34
D) 4x2+44 x ^ { 2 } + 4
E) 2x2+42 x ^ { 2 } + 4
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
38
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 , compounded 4 times per year. Round the answer to two decimal places.

A)$3,161.40
B)$12,000.00
C)$12,645.59
D)$94,298.50
E)$6,392.88
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
39
Identify the transformation of f(x)=15xf ( x ) = 15 ^ { x } . h(x)=15xh ( x ) = - 15 ^ { x }

A)a reflection about the y -axis
B)a reflection about the x -axis
C)a reflection about the line y=-x
D)a reflection about the line y=x
E)a reflection about the line x=15
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
40
Determine the principal P (to the nearest cent)that will yield a balance of <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded 4 times per year. Round the answer to two decimal places.</strong> A)$173,611.11 B)$14,218.75 C)$1,026,614.38 D)$147,569.44 E)$71,090.14 dollars when invested at rate <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded 4 times per year. Round the answer to two decimal places.</strong> A)$173,611.11 B)$14,218.75 C)$1,026,614.38 D)$147,569.44 E)$71,090.14 for 40 years, compounded 4 times per year. Round the answer to two decimal places.

A)$173,611.11
B)$14,218.75
C)$1,026,614.38
D)$147,569.44
E)$71,090.14
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
41
Use the function of f(x)={(2,3),(1,1),(0,0),(1,1),(2,3)}f ( x ) = \{ ( - 2,3 ) , ( - 1,1 ) , ( 0,0 ) , ( 1 , - 1 ) , ( 2 , - 3 ) \} and g(x)={(3,2),(1,3),(0,3),(2,4),(3,4)}g ( x ) = \{ ( - 3 , - 2 ) , ( - 1 , - 3 ) , ( 0,3 ) , ( 2,4 ) , ( 3,4 ) \} to find the value of (gf)(2)( g \circ f ) ( - 2 ) .

A)4
B)3
C)-3
D)2
E)-2
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
42
Find the inverse function of f(x)=6xf ( x ) = 6 - x .

A) f1(x)=6xf ^ { - 1 } ( x ) = 6 - x
B) f1(x)=6xf ^ { - 1 } ( x ) = - 6 - x
C) f1(x)=6f ^ { - 1 } ( x ) = 6
D) f1(x)=6+xf ^ { - 1 } ( x ) = 6 + x
E) f1(x)=6+xf ^ { - 1 } ( x ) = - 6 + x
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
43
Find the inverse function of f(x)=47xf ( x ) = 4 - 7 x .

A) f1(x)=17x4f ^ { - 1 } ( x ) = \frac { 1 } { 7 } x - 4
B) f1(x)=4x7f ^ { - 1 } ( x ) = \frac { 4 - x } { 7 }
C) f1(x)=17x+4f ^ { - 1 } ( x ) = \frac { 1 } { 7 } x + 4
D) f1(x)=x47f ^ { - 1 } ( x ) = \frac { x - 4 } { 7 }
E)The function does not have an inverse.
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
44
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.
 <strong>Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.    f ( x ) = \sqrt { 81 - x ^ { 2 } } </strong> A)f is one-to-one B)f is not one-to-one C)cannot be determined
f(x)=81x2f ( x ) = \sqrt { 81 - x ^ { 2 } }

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
45
Which statement(s)verify that f(x)=4x+1f ( x ) = \frac { 4 } { x + 1 } and g(x)=4xxg ( x ) = \frac { 4 - x } { x } are inverse?

A) f(x)+g(x)=4x+1+4xx=0f ( x ) + g ( x ) = \frac { 4 } { x + 1 } + \frac { 4 - x } { x } = 0
B) f(x)g(x)=4x+14xx=1\frac { f ( x ) } { g ( x ) } = \frac { \frac { 4 } { x + 1 } } { \frac { 4 - x } { x } } = 1
C) f(g(x))=44xx+1=x,g(f(x))=44x+14x+1=xf ( g ( x ) ) = \frac { 4 } { \frac { 4 - x } { x } + 1 } = x , g ( f ( x ) ) = \frac { 4 - \frac { 4 } { x + 1 } } { \frac { 4 } { x + 1 } } = x
D) f(x)+g(x)=4x+1+4xx=1f ( x ) + g ( x ) = \frac { 4 } { x + 1 } + \frac { 4 - x } { x } = 1
E) f(g(x))=44xx+1=1;g(f(x))=4x+14x+1=1f ( g ( x ) ) = \frac { 4 } { \frac { 4 - x } { x } + 1 } = 1 ; g ( f ( x ) ) = \frac { \frac { 4 } { x + 1 } } { \frac { 4 } { x + 1 } } = 1
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
46
Find the domain of gfg \circ f where f(x)=xx5f ( x ) = \frac { x } { x - 5 } and g(x)=xg ( x ) = \sqrt { x } .

A) [0,5)(5,)[ 0,5 ) \cup ( 5 , \infty )
B) (25,)( 25 , \infty )
C) (,0](5,)( - \infty , 0 ] \cup ( 5 , \infty )
D) [0,25)(25,)[ 0,25 ) \cup ( 25 , \infty )
E) (,25)(25,)( - \infty , 25 ) \cup ( 25 , \infty )
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
47
Find the domain of gfg \circ f where f(x)=x2f ( x ) = \sqrt { x - 2 } and g(x)=x+6g ( x ) = x + 6 .

A) [2,)[ 2 , \infty )
B) [4,)[ 4 , \infty )
C) [4,)[ - 4 , \infty )
D) [6,)[ - 6 , \infty )
E) [0,)[ 0 , \infty )
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
48
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.
 <strong>Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.    f ( x ) = 5 \sqrt { - x } </strong> A)f is one-to-one B)f is not one-to-one C)cannot be determined
f(x)=5xf ( x ) = 5 \sqrt { - x }

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
49
Which statement(s)verify that f(x)=9x1f ( x ) = 9 x - 1 and g(x)=19(x+1)g ( x ) = \frac { 1 } { 9 } ( x + 1 ) are inverse?

A) f(x)g(x)=(9x1)19(x+1)=1f ( x ) \cdot g ( x ) = ( 9 x - 1 ) \frac { 1 } { 9 } ( x + 1 ) = - 1
B) f(g(x))=(9(19x)+1)1=x,g(f(x))=19(9(x1)+1)=xf ( g ( x ) ) = \left( 9 \left( \frac { 1 } { 9 } x \right) + 1 \right) - 1 = x , g ( f ( x ) ) = \frac { 1 } { 9 } ( 9 ( x - 1 ) + 1 ) = x
C) f(g(x))=(9(19x)+1)1=x;g(f(x))=19((9x1)+1)=xf ( g ( x ) ) = \left( 9 \left( \frac { 1 } { 9 } x \right) + 1 \right) - 1 = x ; g ( f ( x ) ) = \frac { 1 } { 9 } ( ( 9 x - 1 ) + 1 ) = x
D) f(g(x))=9(19(x+1))1=x;g(f(x))=19((9x1)+1)=xf ( g ( x ) ) = 9 \left( \frac { 1 } { 9 } ( x + 1 ) \right) - 1 = x ; g ( f ( x ) ) = \frac { 1 } { 9 } ( ( 9 x - 1 ) + 1 ) = x
E) f(x)g(x)=9(x1)9(x+1)=1\frac { f ( x ) } { g ( x ) } = \frac { 9 ( x - 1 ) } { 9 ( x + 1 ) } = - 1
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
50
Find (gf)(5)( g \circ f ) ( - 5 ) where f(x)=3x+4f ( x ) = 3 x + 4 and g(x)=x26g ( x ) = x ^ { 2 } - 6 .

A)73
B)115
C)223
D)61
E)-9
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
51
Find the domain of gfg \circ f where f(x)=xx64f ( x ) = \frac { x } { x - 64 } and g(x)=xg ( x ) = \sqrt { x } .

A) (0,64](64,)( 0,64 ] \cup ( 64 , \infty )
B) (,0](64,)( - \infty , 0 ] \cup ( 64 , \infty )
C) [0,8)(8,)[ 0,8 ) \cup ( 8 , \infty )
D) (0,)( 0 , \infty )
E) (0,)( 0 , \infty ) .
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
52
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x+7f ( x ) = 4 x + 7 and g(x)=x21g ( x ) = x ^ { 2 } - 1 .

A) 4x328x24x74 x ^ { 3 } 28 x ^ { 2 } - 4 x - 7
B) 4x2+34 x ^ { 2 } + 3
C) 16x2+56x+4816 x ^ { 2 } + 56 x + 48
D) 16x2+616 x ^ { 2 } + 6
E) 4x2+64 x ^ { 2 } + 6
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
53
Find the inverse function of f(t)=t75f ( t ) = t ^ { 7 } - 5 .

A) f1(t)=t57f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t - 5 }
B) f1(t)=t75f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t } - 5
C) f1(t)=t+57f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t + 5 }
D) f1(t)=t7+5f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t } + 5
E)The function does not have an inverse.
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
54
Find the domain of fgf \circ g where f(x)=x7f ( x ) = \sqrt { x - 7 } and g(x)=x+5g ( x ) = x + 5 .

A) [5,)[ - 5 , \infty )
B) [0,)[ 0 , \infty )
C) [7,)[ 7 , \infty )
D) [2,)[ - 2 , \infty )
E) [2,)[ 2 , \infty )
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
55
Find (gf)(3)( g \circ f ) ( 3 ) where f(x)=2x11f ( x ) = 2 x - 11 and g(x)=x+6g ( x ) = \sqrt { x + 6 } .

A)-16
B)2
C)1
D)-15
E)-5
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
56
Find (fg)(3)( f \circ g ) ( 3 ) where f(x)=2x38f ( x ) = 2 x - 38 and g(x)=x+33g ( x ) = \sqrt { x + 33 } .

A)-64
B)-26
C)-5
D)-192
E)1
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
57
Which statement(s)verify that f(x)=x+47f ( x ) = \sqrt [ 7 ] { x + 4 } and g(x)=x24g ( x ) = x ^ { 2 } - 4 are inverse?

A) f(g(x))=x74+47=x;g(f(x))=(x7)7+44=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } - 4 + 4 } = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x } ) ^ { 7 } + 4 - 4 = x
B) f(x)g(x)=x+47(x74)=xf ( x ) \cdot g ( x ) = \sqrt [ 7 ] { x + 4 } \cdot \left( x ^ { 7 } - 4 \right) = x
C) f(g(x))=x774+4=x;g(f(x))=(x+47)74=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } } - 4 + 4 = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x + 4 } ) ^ { 7 } - 4 = x
D) f(g(x))=x74+47=x;g(f(x))=(x+47)74=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } - 4 + 4 } = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x + 4 } ) ^ { 7 } - 4 = x
E) f(x)g(x)=x+47x7b=1\frac { f ( x ) } { g ( x ) } = \frac { \sqrt [ 7 ] { x + 4 } } { x ^ { 7 } - b } = - 1
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
58
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x8f ( x ) = 4 x - 8 and g(x)=x+4g ( x ) = \sqrt { x + 4 } .

A) 4x44 \sqrt { x - 4 }
B) 4x4\sqrt { 4 x - 4 }
C) 4x+168\sqrt { 4 x + 16 } - 8
D) (4x8)x+4( 4 x - 8 ) \sqrt { x + 4 }
E) 4x+484 \sqrt { x + 4 } - 8
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
59
Find (fg)(x)( f \circ g ) ( x ) where f(x)=4x3f ( x ) = 4 x - 3 and g(x)=x+8g ( x ) = \sqrt { x + 8 } .

A) 4x+834 \sqrt { x + 8 } - 3
B) 4x+5\sqrt { 4 x + 5 }
C) 4x+323\sqrt { 4 x + 32 } - 3
D) 4x+54 \sqrt { x + 5 }
E) (4x3)x+8( 4 x - 3 ) \sqrt { x + 8 }
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
60
Find (fg)(3)( f \circ g ) ( - 3 ) where f(x)=4x+6f ( x ) = 4 x + 6 and g(x)=x24g ( x ) = x ^ { 2 } - 4 .

A)32
B)38
C)146
D)132
E)26
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
61
Match f(x)=log2(x+3)f ( x ) = \log _ { 2 } ( x + 3 ) with its graph.

A)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
62
Match f(x)=log4(x)f ( x ) = \log _ { 4 } ( - x ) with its graph.

A)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
63
Write the exponential equation 7292/3=81729 ^ { 2 / 3 } = 81 in logarithmic form.

A) log72981=23\log _ { 729 } 81 = \frac { 2 } { 3 }
B) log9729=9\log _ { 9 } 729 = 9
C) log981=2\log _ { 9 } 81 = 2
D) log72981=32\log _ { 729 } 81 = \frac { 3 } { 2 }
E) log72981=3\log _ { 729 } 81 = 3
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
64
Identify the vertical asymptote of g(t)=log5tg ( t ) = - \log _ { 5 } t .

A) t=5
B) t=15t = - \frac { 1 } { 5 }
C) t=15t = \frac { 1 } { 5 }
D) t=-5
E)y -axis
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
65
Evaluate the logarithm. log6416\log _ { 64 } 16

A) 12\frac { 1 } { 2 }
B) 3
C) 2
D) 23\frac { 2 } { 3 }
E) log6416\log _ { 64 } 16 is undefined.
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
66
Use a calculator to evaluate the common logarithm log1047\log _ { 10 } 47 . Round your answer to four decimal places.

A)1.6812
B)1.6721
C)3.8501
D)1.9777
E)3.8712
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
67
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
68
Find the inverse function of f(x)=x+5,x5f ( x ) = \sqrt { x + 5 } , x \geq - 5 .

A) f1(x)=x25,x0f ^ { - 1 } ( x ) = x ^ { 2 } - 5 , x \geq 0
B) f1(x)=x225,x0f ^ { - 1 } ( x ) = x ^ { 2 } - 25 , x \geq 0
C) f1(x)=(x25)2f ^ { - 1 } ( x ) = ( x - 25 ) ^ { 2 }
D) f1(x)=(x5)2f ^ { - 1 } ( x ) = ( x - 5 ) ^ { 2 }
E)The function does not have an inverse.
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
69
Evaluate the logarithm. log9(0)\log _ { 9 } ( 0 )

A) 19\frac { 1 } { 9 }
B)1
C) -1
D)0
E)Undefined
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
70
Identify the vertical asymptote of g(t)=6+log7tg ( t ) = - 6 + \log _ { 7 } t .

A) t=-6
B) t=6
C) t=7
D) t=-7
E)y -axis
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
71
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
72
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
73
Evaluate the logarithm. log36216\log _ { 36 } 216

A) 32\frac { 3 } { 2 }
B)3
C) 23\frac { 2 } { 3 }
D)6
E) log36216\log _ { 36 } 216 is undefined.
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
74
Match f(x)=3+log5xf ( x ) = 3 + \log _ { 5 } x with its graph.

A)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
75
Match f(x)=log2xf ( x ) = - \log _ { 2 } x with its graph.

A)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
76
Evaluate the logarithm. log3[27]\log _ { 3 } [ 27 ]

A) -3
B)9
C) log327\log _ { 3 } 27
D)3
E) log327\log _ { 3 } 27 is undefined.
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
77
Evaluate the logarithm. log6(6)\log _ { 6 } ( - 6 )

A)0
B) 16\frac { 1 } { 6 }
C) -1
D) e1e^ { - 1 }
E) log6(6)\log _ { 6 } ( - 6 ) is undefined.
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
78
Write the logarithmic equation log2132=5\log _ { 2 } \frac { 1 } { 32 } = - 5 in exponential form.

A) 25=1322 ^ { - 5 } = \frac { 1 } { 32 }
B) 25=1322 ^ { - 5 } = - \frac { 1 } { 32 }
C) 52=1105 ^ { 2 } = \frac { 1 } { 10 }
D) 52=325 ^ { 2 } = 32
E) 25=152 ^ { - 5 } = \frac { 1 } { 5 }
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
79
Evaluate the logarithm. log51125\log _ { 5 } \frac { 1 } { 125 }

A) 3\sqrt { 3 }
B) -3
C)0
D) 13\frac { 1 } { 3 }
E) log51125\log _ { 5 } \frac { 1 } { 125 } is undefined.
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
80
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
locked card icon
Unlock Deck
Unlock for access to all 165 flashcards in this deck.