Question 1

Graph the relation using solid circles and the inverse using open circles.
-{(-8, -5), (5, 8), (9, 9), (-9, -9)}

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 2

Find an equation of the inverse of the relation.
-$$y = 2 x ^ { 3 } + 4$$

Accepted Answer

A)  $y = 4 x ^ { 3 } + 2$ 
B)  $x = 2 y ^ { 3 } + 4$ 
C)  $x = 4 y ^ { 3 } + 2$ 
D)  $y = - 2 x ^ { 3 } - 4$ 
A)  $y = 4 x ^ { 3 } + 2$ 
B)  $x = 2 y ^ { 3 } + 4$ 
C)  $x = 4 y ^ { 3 } + 2$ 
D)  $y = - 2 x ^ { 3 } - 4$

Question 3

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$.
-$$h ( x ) = 6 ( 3 x + 8 ) ^ { 2 } - 9$$

Accepted Answer

A)  $f ( x ) = ( 6 x - 9 ) ^ { 2 } , g ( x ) = 3 x + 8$ 
B)  $f ( x ) = 6 x ^ { 2 } - 9 , g ( x ) = ( 3 x + 8 ) ^ { 2 }$ 
C)  $f ( x ) = 3 x + 8 , g ( x ) = 6 x ^ { 2 } - 9$ 
D)  $f ( x ) = 6 x ^ { 2 } - 9 , g ( x ) = 3 x + 8$ 
A)  $f ( x ) = ( 6 x - 9 ) ^ { 2 } , g ( x ) = 3 x + 8$ 
B)  $f ( x ) = 6 x ^ { 2 } - 9 , g ( x ) = ( 3 x + 8 ) ^ { 2 }$ 
C)  $f ( x ) = 3 x + 8 , g ( x ) = 6 x ^ { 2 } - 9$ 
D)  $f ( x ) = 6 x ^ { 2 } - 9 , g ( x ) = 3 x + 8$

Question 4

Solve the problem.
-A computer is purchased for $\$ 4700$. Its value each year is about $78 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $\mathrm { V } ( \mathrm { t } ) = 4700 ( 0.78 ) ^ { \mathrm { t } }$. Find the value of the computer after 7 years.

Accepted Answer

A)  $\$ 643.95$ 
B)  $\$ 502.28$ 
C)  $\$ 825.58$ 
D)  $\$ 25,662.00$ 
A)  $\$ 643.95$ 
B)  $\$ 502.28$ 
C)  $\$ 825.58$ 
D)  $\$ 25,662.00$

Question 5

Find the requested composition of functions.
-Given $f ( x ) = - 2 x + 8$ and $g ( x ) = 4 x + 7$, find $g \circ f ( x )$.

Accepted Answer

A)  $- 8 x + 39$ 
B)  $x - 39$ 
C)  $x + 39$ 
D)  $- 8 x + 22$ 
A)  $- 8 x + 39$ 
B)  $x - 39$ 
C)  $x + 39$ 
D)  $- 8 x + 22$

Question 6

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
-$$f ( x ) = 5 x ^ { 3 } + 3$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } + 3 } { 5 } }$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x - 3 } { 5 } }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x } { 5 } } - 3$ 
D)  Not a one-to-one function 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } + 3 } { 5 } }$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x - 3 } { 5 } }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x } { 5 } } - 3$ 
D)  Not a one-to-one function

Question 7

Graph.
-$f(x)=\left(\frac{1}{2}\right)^{x}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$.
-$$h ( x ) = \frac { 1 } { x ^ { 2 } - 8 }$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 8 }$ 
B)  $f ( x ) = \frac { 1 } { 8 } , g ( x ) = x ^ { 2 } - 8$ 
C)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 8$ 
D)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 8$ 
A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 8 }$ 
B)  $f ( x ) = \frac { 1 } { 8 } , g ( x ) = x ^ { 2 } - 8$ 
C)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 8$ 
D)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 8$

Question 9

Use composition to verify whether or not the inverse is correct.
-$$f ( x ) = 3 x + 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3$$

Accepted Answer

A) True 
 B)False

Question 10

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$.
-$$h ( x ) = ( - 8 x - 9 ) ^ { 6 }$$

Accepted Answer

A)  $f ( x ) = - 8 x - 9 , g ( x ) = x ^ { 6 }$ 
B)  $f ( x ) = ( - 8 x ) ^ { 6 } , g ( x ) = - 9$ 
C)  $f ( x ) = x ^ { 6 } , g ( x ) = - 8 x - 9$ 
D)  $f ( x ) = - 8 x 6 , g ( x ) = x - 9$ 
A)  $f ( x ) = - 8 x - 9 , g ( x ) = x ^ { 6 }$ 
B)  $f ( x ) = ( - 8 x ) ^ { 6 } , g ( x ) = - 9$ 
C)  $f ( x ) = x ^ { 6 } , g ( x ) = - 8 x - 9$ 
D)  $f ( x ) = - 8 x 6 , g ( x ) = x - 9$

Question 11

Find an equation of the inverse of the relation.
-$$y = 7 x ^ { 2 } + 4 x$$

Accepted Answer

A)  $x = 7 y ^ { 2 } + 4 y$ 
B)  $y = - 7 x ^ { 2 } - 4 x$ 
C)  $x = 4 y ^ { 2 } + 7 y$ 
D)  $y = 4 x ^ { 2 } + 7 x$ 
A)  $x = 7 y ^ { 2 } + 4 y$ 
B)  $y = - 7 x ^ { 2 } - 4 x$ 
C)  $x = 4 y ^ { 2 } + 7 y$ 
D)  $y = 4 x ^ { 2 } + 7 x$

Question 12

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
-$$f ( x ) = x ^ { 3 } + 1$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 1 }$ 
B)  Not a one-to-one function 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 1 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 1$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 1 }$ 
B)  Not a one-to-one function 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 1 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 1$

Question 13

Determine whether the function is one-to-one.
-$$f ( x ) = x ^ { 2 } + 3$$

Accepted Answer

A) True 
 B)False

Question 14

Graph.
-$f(x)=4^{x-4}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 15

Graph the relation using solid circles and the inverse using open circles.
-{(-10, 14), (-17, -13), (18, 3)}

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 16

Determine whether the function is one-to-one.
-f(x)= 2x - 4

Accepted Answer

A) True 
 B)False

Question 17

Solve the problem.
-The amount of particulate matter left in solution during a filtering process decreases by the equation $P ( n ) = 600 ( 0.5 ) ^ { 0.8 n }$, where $n$ is the number of filtering steps. Find the amounts left for $n = 0$ and $n = 5$. (Round to the nearest whole number.)

Accepted Answer

A)  $1200 ; 38$ 
B)  $600 ; 19$ 
C)  $600 ; 9600$ 
D)  $600 ; 38$ 
A)  $1200 ; 38$ 
B)  $600 ; 19$ 
C)  $600 ; 9600$ 
D)  $600 ; 38$

Question 18

Graph the function as a solid curve and its inverse as a dashed curve.
-$f(x)=x^{3}+5$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Find the requested composition of functions.
-Given $f ( x ) = \frac { 2 } { x ^ { 2 } }$ and $g ( x ) = x - 3$, find $g \circ f ( x )$

Accepted Answer

A)  $\frac { - 1 } { x ^ { 2 } }$ 
B)  $\frac { 2 } { x ^ { 2 } - 3 }$ 
C)  $\frac { 2 } { ( x - 3 ) ^ { 2 } }$ 
D)  $\frac { 2 } { x ^ { 2 } } - 3$ 
A)  $\frac { - 1 } { x ^ { 2 } }$ 
B)  $\frac { 2 } { x ^ { 2 } - 3 }$ 
C)  $\frac { 2 } { ( x - 3 ) ^ { 2 } }$ 
D)  $\frac { 2 } { x ^ { 2 } } - 3$

Question 20

Solve the problem.
-The number of bacteria growing in an incubation culture increases with time according to $B ( x ) = 5300 ( 2 ) ^ { X }$, where $x$ is time in days. Find the number of bacteria when $x = 0$ and $x = 5$.

Accepted Answer

A)  10,$600 ; 169,600$ 
B)  $5300 ; 21,200$ 
C)  $5300 ; 169,600$ 
D)  $5300 ; 53,000$ 
A)  10,$600 ; 169,600$ 
B)  $5300 ; 21,200$ 
C)  $5300 ; 169,600$ 
D)  $5300 ; 53,000$

Graph the relation using solid circles and the inverse using open circles. -{(-8, -5), (5, 8), (9, 9), (-9, -9)}

Find an equation of the inverse of the relation. - $y = 2 x ^ { 3 } + 4$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = 6 ( 3 x + 8 ) ^ { 2 } - 9$

Find the requested composition of functions. -Given $f ( x ) = - 2 x + 8$ and $g ( x ) = 4 x + 7$ , find $g \circ f ( x )$ .

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = 5 x ^ { 3 } + 3$

Graph. - $f(x)=\left(\frac{1}{2}\right)^{x}$ $Graph. - f(x)=\left(\frac{1}{2}\right)^{x}$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = \frac { 1 } { x ^ { 2 } - 8 }$

Use composition to verify whether or not the inverse is correct. - $f ( x ) = 3 x + 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = ( - 8 x - 9 ) ^ { 6 }$

Find an equation of the inverse of the relation. - $y = 7 x ^ { 2 } + 4 x$

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = x ^ { 3 } + 1$

Determine whether the function is one-to-one. - $f ( x ) = x ^ { 2 } + 3$

Graph. - $f(x)=4^{x-4}$ $Graph. - f(x)=4^{x-4}$

Graph the relation using solid circles and the inverse using open circles. -{(-10, 14), (-17, -13), (18, 3)}

Determine whether the function is one-to-one. -f(x)= 2x - 4

Solve the problem. -The amount of particulate matter left in solution during a filtering process decreases by the equation $P ( n ) = 600 ( 0.5 ) ^ { 0.8 n }$ , where $n$ is the number of filtering steps. Find the amounts left for $n = 0$ and $n = 5$ . (Round to the nearest whole number.)

Graph the function as a solid curve and its inverse as a dashed curve. - $f(x)=x^{3}+5$ $Graph the function as a solid curve and its inverse as a dashed curve. - f(x)=x^{3}+5$

Find the requested composition of functions. -Given $f ( x ) = \frac { 2 } { x ^ { 2 } }$ and $g ( x ) = x - 3$ , find $g \circ f ( x )$

Solve the problem. -The number of bacteria growing in an incubation culture increases with time according to $B ( x ) = 5300 ( 2 ) ^ { X }$ , where $x$ is time in days. Find the number of bacteria when $x = 0$ and $x = 5$ .

Introduction to Real Numbers and Algebraic Expressions

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Graphs of Linear Equations

Polynomials: Operations

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Exam 12: Exponential Functions and Logarithmic Functions

Graph the relation using solid circles and the inverse using open circles. -{(-8, -5), (5, 8), (9, 9), (-9, -9)}

Find an equation of the inverse of the relation. - y=2x3+4y = 2 x ^ { 3 } + 4y=2x3+4

Find f(x) and g(x) such that h(x) = (f∘g)(x)(f \circ g)(x)(f∘g)(x) . - h(x)=6(3x+8)2−9h ( x ) = 6 ( 3 x + 8 ) ^ { 2 } - 9h(x)=6(3x+8)2−9

Find the requested composition of functions. -Given f(x)=−2x+8f ( x ) = - 2 x + 8f(x)=−2x+8 and g(x)=4x+7g ( x ) = 4 x + 7g(x)=4x+7 , find g∘f(x)g \circ f ( x )g∘f(x) .

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - f(x)=5x3+3f ( x ) = 5 x ^ { 3 } + 3f(x)=5x3+3

Graph. - f(x)=(12)xf(x)=\left(\frac{1}{2}\right)^{x}f(x)=(21​)x

Find f(x) and g(x) such that h(x) = (f∘g)(x)(f \circ g)(x)(f∘g)(x) . - h(x)=1x2−8h ( x ) = \frac { 1 } { x ^ { 2 } - 8 }h(x)=x2−81​

Use composition to verify whether or not the inverse is correct. - f(x)=3x+9,f−1(x)=13x−3f ( x ) = 3 x + 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3f(x)=3x+9,f−1(x)=31​x−3

Find f(x) and g(x) such that h(x) = (f∘g)(x)(f \circ g)(x)(f∘g)(x) . - h(x)=(−8x−9)6h ( x ) = ( - 8 x - 9 ) ^ { 6 }h(x)=(−8x−9)6

Find an equation of the inverse of the relation. - y=7x2+4xy = 7 x ^ { 2 } + 4 xy=7x2+4x

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - f(x)=x3+1f ( x ) = x ^ { 3 } + 1f(x)=x3+1

Determine whether the function is one-to-one. - f(x)=x2+3f ( x ) = x ^ { 2 } + 3f(x)=x2+3

Graph. - f(x)=4x−4f(x)=4^{x-4}f(x)=4x−4

Graph the relation using solid circles and the inverse using open circles. -{(-10, 14), (-17, -13), (18, 3)}

Determine whether the function is one-to-one. -f(x)= 2x - 4

Graph the function as a solid curve and its inverse as a dashed curve. - f(x)=x3+5f(x)=x^{3}+5f(x)=x3+5

Find the requested composition of functions. -Given f(x)=2x2f ( x ) = \frac { 2 } { x ^ { 2 } }f(x)=x22​ and g(x)=x−3g ( x ) = x - 3g(x)=x−3 , find g∘f(x)g \circ f ( x )g∘f(x)

Solve the problem. -The number of bacteria growing in an incubation culture increases with time according to B(x)=5300(2)XB ( x ) = 5300 ( 2 ) ^ { X }B(x)=5300(2)X , where xxx is time in days. Find the number of bacteria when x=0x = 0x=0 and x=5x = 5x=5 .

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Filters

Find an equation of the inverse of the relation. - $y = 2 x ^ { 3 } + 4$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = 6 ( 3 x + 8 ) ^ { 2 } - 9$

Find the requested composition of functions. -Given $f ( x ) = - 2 x + 8$ and $g ( x ) = 4 x + 7$ , find $g \circ f ( x )$ .

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = 5 x ^ { 3 } + 3$

Graph. - $f(x)=\left(\frac{1}{2}\right)^{x}$ $Graph. - f(x)=\left(\frac{1}{2}\right)^{x}$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = \frac { 1 } { x ^ { 2 } - 8 }$

Use composition to verify whether or not the inverse is correct. - $f ( x ) = 3 x + 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3$

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$ . - $h ( x ) = ( - 8 x - 9 ) ^ { 6 }$

Find an equation of the inverse of the relation. - $y = 7 x ^ { 2 } + 4 x$

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = x ^ { 3 } + 1$

Determine whether the function is one-to-one. - $f ( x ) = x ^ { 2 } + 3$

Graph. - $f(x)=4^{x-4}$ $Graph. - f(x)=4^{x-4}$

Graph the function as a solid curve and its inverse as a dashed curve. - $f(x)=x^{3}+5$ $Graph the function as a solid curve and its inverse as a dashed curve. - f(x)=x^{3}+5$

Find the requested composition of functions. -Given $f ( x ) = \frac { 2 } { x ^ { 2 } }$ and $g ( x ) = x - 3$ , find $g \circ f ( x )$

Solve the problem. -The number of bacteria growing in an incubation culture increases with time according to $B ( x ) = 5300 ( 2 ) ^ { X }$ , where $x$ is time in days. Find the number of bacteria when $x = 0$ and $x = 5$ .