Question 1

Solve the problem.
-The half-life of Antimony 111 is $2.9$ hours. If the formula $\mathrm { P } ( \mathrm { t } ) = \left( \frac { 1 } { 2 } \right) ^ { t / 2.9 }$ gives the percent (as a decimal) remaining after time $t$ (in hours), sketch P versus $t$.

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 2

Find the inverse of the relation.
-{(6, -6), (6, -5), (4, -4), (2, -3)}

Accepted Answer

A) {(-6, 6), (-5, 6), (-4, 4), (-3, 2)} 
B) {(-5, -6), (-6, 4), (6, 6), (-5, -4)} 
C) {(-5, -6), (-3, 4), (6, 4), (-5, -4)}

Question 3

Solve the problem.
-An accountant tabulated a firm's profits for four recent years in the following table:

The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the linear graph to estimate the profits in the year $2001 .$

Accepted Answer

A)  About $\$ 500,000$ 
B)  About $\$ 800,000$ 
C)  About $\$ 900,000$ 
D)  About $\$ 700,000$

Question 4

Determine whether the function is one-to-one.
-$$f ( x ) = 7 x ^ { 2 } + 3$$

Accepted Answer

A) True 
 B)False

Question 5

Determine whether the function is one-to-one.
-$$f ( x ) = 4 x ^ { 2 } + x$$

Accepted Answer

A) True 
 B)False

Question 6

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
-$$y = 2 x ^ { 2 } + 4 x$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 7

Determine whether the function is one-to-one.
-$$f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$$

Accepted Answer

A) True 
 B)False

Question 8

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
-$$y = 4 x ^ { 3 } + 7$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 9

Determine whether the function is one-to-one.
-$$f ( x ) = x ^ { 3 } - 7$$

Accepted Answer

A) True 
 B)False

Question 10

Graph.
-$f(x)=4^{3 x-2}$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 11

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$.
-$$h ( x ) = \frac { 8 } { \sqrt { 5 x + 4 } }$$

Accepted Answer

A)  $f ( x ) = \frac { 8 } { x } , g ( x ) = 5 x + 4$ 
B)  $f ( x ) = 8 , g ( x ) = \sqrt { 5 + 4 }$ 
C)  $f ( x ) = \frac { 8 } { \sqrt { x } } , g ( x ) = 5 x + 4$ 
D)  $f ( x ) = \sqrt { 5 x + 4 } , g ( x ) = 8$

Question 12

Determine whether the function is one-to-one.
-$$f ( x ) = 16 - x ^ { 2 }$$

Accepted Answer

A) True 
 B)False

Question 13

Graph.
-$$x = 6 y$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 14

Find f(x) and g(x) such that h(x) = $(f \circ g)(x)$.
-$$h ( x ) = ( \sqrt { x } - 7 ) ^ { 2 }$$

Accepted Answer

A)  $f ( x ) = x ^ { 2 } , g ( x ) = \sqrt { x } - 7$ 
B)  $f ( x ) = \sqrt { x } - 7 , g ( x ) = x ^ { 2 }$ 
C)  $f ( x ) = \sqrt { x ^ { 2 } } , g ( x ) = x - 7$ 
D)  $f ( x ) = \sqrt { x } , g ( x ) = ( x - 7 ) ^ { 2 }$

Question 15

Solve the problem.
-The half-life of a certain radioactive substance is 22 years. Suppose that at time $t = 0$, there are $24 \mathrm {~g}$ of the substance. Then after t years, the number of grams of the substance remaining will be:
$N ( t ) = 24 \left( \frac { 1 } { 2 } \right) ^ { t / 44 }$
How many grams of the substance will remain after 242 years? Round to the nearest hundredth when necessary.

Accepted Answer

A)  $0.53 \mathrm {~g}$ 
B)  $0.07 \mathrm {~g}$ 
C)  $0.27 \mathrm {~g}$ 
D)  $0.13 \mathrm {~g}$

Question 16

Solve the problem.
-Suppose that $90,000 is invested at 4% interest, compounded annually. Find a function A for the amount in the account after t years.

Accepted Answer

A)  $\mathrm { A } ( \mathrm { t } ) = \$ 90,000 ( 1.04 ) ^ { \mathrm { t } }$ 
B)  $\mathrm { A } ( \mathrm { t } ) = \$ 90,000 ( 0.04 ) ^ { \mathrm { t } }$ 
C)  $\mathrm { A } ( \mathrm { t } ) = \$ 90,000^{0.04} \mathrm { t }$ 
D)  $\mathrm { A } ( \mathrm { t } ) = \$ 90,000 ^ { 1.04 \mathrm { t } }$

Question 17

Solve the problem.
-A size 10 dress in Country C is size 44 in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = 2 ( x + 12 )$. Find a formula for the inverse of the function described.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x - 12 } { 2 }$ 
B)  $f ^ { - 1 } ( x ) = x - 12$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 2 } + 12$ 
D)  $f ^ { - 1 } ( x ) = \frac { x } { 2 } - 12$

Question 18

Find the inverse of the relation.
-{(-6, 2), (-2, 6), (9, -2), (-9, 2)}

Accepted Answer

A) {(2, -6), (6, -2), (-2, 9), (2, -9)} 
B) {(2, 9), (9, -2), (2, -6), (-2, -9)} 
C) {(2, 9), (6, -2), (2, -2), (-2, -9)}

Question 19

Use composition to verify whether or not the inverse is correct.
-$$f ( x ) = 3 x + 6 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3$$

Accepted Answer

A) True 
 B)False

Question 20

Find an equation of the inverse of the relation.
-y = 6x + 5

Accepted Answer

A) x = 5y + 6 
B) y = 5x + 6 
C) y = -6x - 5 
D) x = 6y + 5

Exam 12: Exponential Functions and Logarithmic Functions

Find the inverse of the relation. -{(6, -6) , (6, -5) , (4, -4) , (2, -3) }

Determine whether the function is one-to-one. - $f ( x ) = 7 x ^ { 2 } + 3$

Determine whether the function is one-to-one. - $f ( x ) = 4 x ^ { 2 } + x$

Determine whether the function is one-to-one. - $f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. - $y = 4 x ^ { 3 } + 7$ $Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. - y = 4 x ^ { 3 } + 7 A) B) C) D)$

Determine whether the function is one-to-one. - $f ( x ) = x ^ { 3 } - 7$

Graph. - $f(x) =4^{3 x-2}$ $Graph. - f(x) =4^{3 x-2} A) B) C) D)$

Find f(x) and g(x) such that h(x) = $(f \circ g) (x)$ . - $h ( x ) = \frac { 8 } { \sqrt { 5 x + 4 } }$

Determine whether the function is one-to-one. - $f ( x ) = 16 - x ^ { 2 }$

Graph. - $x = 6 y$

Find f(x) and g(x) such that h(x) = $(f \circ g) (x)$ . - $h ( x ) = ( \sqrt { x } - 7 ) ^ { 2 }$

Solve the problem. -Suppose that $90,000 is invested at 4% interest, compounded annually. Find a function A for the amount in the account after t years.

Solve the problem. -A size 10 dress in Country C is size 44 in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = 2 ( x + 12 )$ . Find a formula for the inverse of the function described.

Find the inverse of the relation. -{(-6, 2) , (-2, 6) , (9, -2) , (-9, 2) }

Use composition to verify whether or not the inverse is correct. - $f ( x ) = 3 x + 6 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3$

Find an equation of the inverse of the relation. -y = 6x + 5

Exam 12: Exponential Functions and Logarithmic Functions

Solve the problem. -The half-life of Antimony 111 is 2.92.92.9 hours. If the formula P(t) =(12) t/2.9\mathrm { P } ( \mathrm { t } ) = \left( \frac { 1 } { 2 } \right) ^ { t / 2.9 }P(t) =(21​) t/2.9 gives the percent (as a decimal) remaining after time ttt (in hours) , sketch P versus ttt .

Find the inverse of the relation. -{(6, -6) , (6, -5) , (4, -4) , (2, -3) }

Determine whether the function is one-to-one. - f(x)=7x2+3f ( x ) = 7 x ^ { 2 } + 3f(x)=7x2+3

Determine whether the function is one-to-one. - f(x)=4x2+xf ( x ) = 4 x ^ { 2 } + xf(x)=4x2+x

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. - y=2x2+4xy = 2 x ^ { 2 } + 4 xy=2x2+4x

Determine whether the function is one-to-one. - f(x)=(17)xf ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }f(x)=(71​)x

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. - y=4x3+7y = 4 x ^ { 3 } + 7y=4x3+7

Determine whether the function is one-to-one. - f(x)=x3−7f ( x ) = x ^ { 3 } - 7f(x)=x3−7

Graph. - f(x) =43x−2f(x) =4^{3 x-2}f(x) =43x−2

Find f(x) and g(x) such that h(x) = (f∘g) (x) (f \circ g) (x) (f∘g) (x) . - h(x) =85x+4h ( x ) = \frac { 8 } { \sqrt { 5 x + 4 } }h(x) =5x+4​8​

Determine whether the function is one-to-one. - f(x)=16−x2f ( x ) = 16 - x ^ { 2 }f(x)=16−x2

Graph. - x=6yx = 6 yx=6y

Find f(x) and g(x) such that h(x) = (f∘g) (x) (f \circ g) (x) (f∘g) (x) . - h(x) =(x−7) 2h ( x ) = ( \sqrt { x } - 7 ) ^ { 2 }h(x) =(x​−7) 2

Solve the problem. -Suppose that $90,000 is invested at 4% interest, compounded annually. Find a function A for the amount in the account after t years.

Solve the problem. -A size 10 dress in Country C is size 44 in Country D. A function that converts dress sizes in Country C to those in Country DDD is f(x) =2(x+12) f ( x ) = 2 ( x + 12 ) f(x) =2(x+12) . Find a formula for the inverse of the function described.

Find the inverse of the relation. -{(-6, 2) , (-2, 6) , (9, -2) , (-9, 2) }

Use composition to verify whether or not the inverse is correct. - f(x)=3x+6,f−1(x)=13x−3f ( x ) = 3 x + 6 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3f(x)=3x+6,f−1(x)=31​x−3

Find an equation of the inverse of the relation. -y = 6x + 5

Determine whether the function is one-to-one. - $f ( x ) = 7 x ^ { 2 } + 3$

Determine whether the function is one-to-one. - $f ( x ) = 4 x ^ { 2 } + x$

Determine whether the function is one-to-one. - $f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. - $y = 4 x ^ { 3 } + 7$ $Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. - y = 4 x ^ { 3 } + 7 A) B) C) D)$

Determine whether the function is one-to-one. - $f ( x ) = x ^ { 3 } - 7$

Graph. - $f(x) =4^{3 x-2}$ $Graph. - f(x) =4^{3 x-2} A) B) C) D)$

Find f(x) and g(x) such that h(x) = $(f \circ g) (x)$ . - $h ( x ) = \frac { 8 } { \sqrt { 5 x + 4 } }$

Determine whether the function is one-to-one. - $f ( x ) = 16 - x ^ { 2 }$

Graph. - $x = 6 y$

Find f(x) and g(x) such that h(x) = $(f \circ g) (x)$ . - $h ( x ) = ( \sqrt { x } - 7 ) ^ { 2 }$

Solve the problem. -A size 10 dress in Country C is size 44 in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = 2 ( x + 12 )$ . Find a formula for the inverse of the function described.

Use composition to verify whether or not the inverse is correct. - $f ( x ) = 3 x + 6 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3$