Question 1

The function f is one-to-one. Find its inverse.
-$$f ( x ) = 7 x ^ { 2 } - 8 , x \geq 0$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { \frac { 7 } { x + 8 } }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 7 } { \sqrt { x } + 8 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \frac { \mathrm { x } + 8 } { 7 } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \sqrt { \frac { \mathrm { x } + 8 } { 7 } }$ 
A)  $f ^ { - 1 } ( x ) = \sqrt { \frac { 7 } { x + 8 } }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 7 } { \sqrt { x } + 8 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \frac { \mathrm { x } + 8 } { 7 } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \sqrt { \frac { \mathrm { x } + 8 } { 7 } }$

Question 2

Use transformations to graph the function.
-$$\text { Use the graph of } \log _ { 5 } x \text { to obtain the graph of } f ( x ) = - 2 \log _ { 5 } x \text {. }$$

Accepted Answer

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

Question 3

Solve the equation.
-$$\log _ { 3 } x + \log _ { 3 } ( x - 24 ) = 4$$

Accepted Answer

A)  No real solutions 
B)  $\{ 53 \}$ 
C)  $\{ 27 \}$ 
D)  $\{ - 3,27 \}$ 
A)  No real solutions 
B)  $\{ 53 \}$ 
C)  $\{ 27 \}$ 
D)  $\{ - 3,27 \}$

Question 4

Choose the one alternative that best completes the statement or answers the question.
The graph of a logarithmic function is shown. Select the function which matches the graph.
-

Accepted Answer

A)  $y = \log ( x ) - 1$ 
B)  $y = \log ( 1 - x )$ 
C)  $y = \log ( x - 1 )$ 
D)  $y = 1 - \log ( x )$ 
A)  $y = \log ( x ) - 1$ 
B)  $y = \log ( 1 - x )$ 
C)  $y = \log ( x - 1 )$ 
D)  $y = 1 - \log ( x )$

Question 5

Use the horizontal line test to determine whether the function is one-to-one.
-

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 6

Write as the sum and/or difference of logarithms. Express powers as factors.
-$\log _ { W } \left( \frac { 13 x } { 2 } \right)$

Accepted Answer

A)  $\log _ { W } 13 + \log _ { w } x + \log _ { W } 2$ 
B)  $\log _ { \mathrm { W } } 13 \mathrm { x } - \log _ { \mathrm { w } } 2$ 
C)  $\log _ { W } 13 + \log _ { W } x - \log _ { W } 2$ 
D)  $\log _ { \mathrm { W } } 11 \mathrm { x }$ 
A)  $\log _ { W } 13 + \log _ { w } x + \log _ { W } 2$ 
B)  $\log _ { \mathrm { W } } 13 \mathrm { x } - \log _ { \mathrm { w } } 2$ 
C)  $\log _ { W } 13 + \log _ { W } x - \log _ { W } 2$ 
D)  $\log _ { \mathrm { W } } 11 \mathrm { x }$

Question 7

The graph of an exponential function is given. Match the graph to one of the following functions.
-

Accepted Answer

A)  $f ( x ) = 2 ^ { x + 2 }$ 
B)  $f ( x ) = 2 ^ { x } - 2$ 
C)  $f ( x ) = 2 ^ { x } + 2$ 
D)  $f ( x ) = 2 ^ { x }$ 
A)  $f ( x ) = 2 ^ { x + 2 }$ 
B)  $f ( x ) = 2 ^ { x } - 2$ 
C)  $f ( x ) = 2 ^ { x } + 2$ 
D)  $f ( x ) = 2 ^ { x }$

Question 8

Choose the one alternative that best completes the statement or answers the question.
-The function $f ( x ) = 300 ( 0.5 ) ^ { x / 90 }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $x$ is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 200 years. Round to the nearest whole number.

Accepted Answer

A)  333 pounds 
B)  220 pounds 
C)  68 pounds 
D)  64 pounds 
A)  333 pounds 
B)  220 pounds 
C)  68 pounds 
D)  64 pounds

Question 9

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$\log _ { x } \left( \frac { 2 } { 5 } \right) = 1$

Accepted Answer

A)  $\left\{ \frac { 2 } { 5 } \right\}$ 
B)  2 
C)  $\left\{ \frac { 5 } { 2 } \right\}$ 
D)  1 
A)  $\left\{ \frac { 2 } { 5 } \right\}$ 
B)  2 
C)  $\left\{ \frac { 5 } { 2 } \right\}$ 
D)  1

Question 10

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function.
-$f(x)=-2^{x+3}+4$

Accepted Answer

A)  domain of $f : ( - \infty , \infty )$; range of $f : ( - \infty , - 4 )$;
asymptote: $\mathrm { y } = - 4$
  
B)  domain of $f : ( - \infty , \infty )$; range of $f : ( - \infty , - 4 )$; horizontal  horizontal asymptote: $\mathrm { y } = - 4$
  
C)  domain of $\mathrm { f } : ( - \infty , \infty )$; range of $\mathrm { f } : ( - 4 , \infty )$;
range of $\mathrm { f } : ( - \infty , 4 )$

D)  domain of $\mathrm { f } : ( - \infty , \infty )$; ; horizontal asymptote: $\mathrm { y } = 4$
  
A)  domain of $f : ( - \infty , \infty )$; range of $f : ( - \infty , - 4 )$;
asymptote: $\mathrm { y } = - 4$
  
B)  domain of $f : ( - \infty , \infty )$; range of $f : ( - \infty , - 4 )$; horizontal  horizontal asymptote: $\mathrm { y } = - 4$
  
C)  domain of $\mathrm { f } : ( - \infty , \infty )$; range of $\mathrm { f } : ( - 4 , \infty )$;
range of $\mathrm { f } : ( - \infty , 4 )$

D)  domain of $\mathrm { f } : ( - \infty , \infty )$; ; horizontal asymptote: $\mathrm { y } = 4$

Question 11

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-$$\text { If } \left. f ( x ) = x ^ { 2 } \text { and } g ( x ) = - 1 + 5 x \text {, find (f } g \right) ( x ) \text { and find the domain of } ( f \circ g ) ( x )$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

Find a formula for the inverse of the function described below.
-$32 ^ { \circ }$ Fahrenheit $= 0 ^ { \circ }$ Celsius. A function that converts temperatures in Celsius to those in Fahrenheit is $f ( x ) = \frac { 9 } { 5 } x + 32$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 9 } { 5 } x + 32$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x - 32 )$ 
C)  $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x + 32 )$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 32$ 
A)  $f ^ { - 1 } ( x ) = \frac { 9 } { 5 } x + 32$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x - 32 )$ 
C)  $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x + 32 )$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 32$

Question 13

Choose the one alternative that best completes the statement or answers the question.
Find the domain of the composite function f ° g.
-$$f ( x ) = \sqrt { 2 - x } ; \quad g ( x ) = | 2 x - 1 |$$

Accepted Answer

A)  $\{ x \mid x \leq 2 \}$ 
B)  $\{ x \mid x \geq 2 \}$ 
C)  $\left\{ x \mid - \frac { 1 } { 2 } \leq x \leq \frac { 3 } { 2 } \right\}$ 
D)  all real numbers 
A)  $\{ x \mid x \leq 2 \}$ 
B)  $\{ x \mid x \geq 2 \}$ 
C)  $\left\{ x \mid - \frac { 1 } { 2 } \leq x \leq \frac { 3 } { 2 } \right\}$ 
D)  all real numbers

Question 14

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function.
-$f(x)=4^{(x-1)}$

Accepted Answer

A)  domain of f: $( - \infty , \infty )$; range of $\mathrm { f } : ( 0 , \infty )$ 
horizontal asymptote: $y = 0$
  
B)  domain of $f : ( - \infty , \infty )$; range of $f : ( 0 , \infty )$ ) horizontal asymptote: $y = 0$
  
C)  domain of $\mathrm { f } : ( - \infty , \infty )$; range of $\mathrm { f } : ( - \infty , 0 )$
 horizontal asymptote: $y = 0$

D)  domain of $f : ( - \infty , \infty )$; range of $f : ( - \infty , 0 )$ horizontal asymptote: $y = 0$
  
A)  domain of f: $( - \infty , \infty )$; range of $\mathrm { f } : ( 0 , \infty )$ 
horizontal asymptote: $y = 0$
  
B)  domain of $f : ( - \infty , \infty )$; range of $f : ( 0 , \infty )$ ) horizontal asymptote: $y = 0$
  
C)  domain of $\mathrm { f } : ( - \infty , \infty )$; range of $\mathrm { f } : ( - \infty , 0 )$
 horizontal asymptote: $y = 0$

D)  domain of $f : ( - \infty , \infty )$; range of $f : ( - \infty , 0 )$ horizontal asymptote: $y = 0$

Question 15

Approximate the value using a calculator. Express answer rounded to three decimal places.
-5.52 $2.828$

Accepted Answer

A)  $310.575$ 
B)  $12,459.589$ 
C)  $15.611$ 
D)  $125.373$ 
A)  $310.575$ 
B)  $12,459.589$ 
C)  $15.611$ 
D)  $125.373$

Question 16

Choose the one alternative that best completes the statement or answers the question.
-Strontium 90 decays at a constant rate of $2.44 \%$ per year. Therefore, the equation for the amount $\mathrm { P }$ of strontium 90 after $t$ years is $\mathrm { P } = \mathrm { P } _ { 0 } \mathrm { e } ^ { - 0.0244 \mathrm { t } }$. How long will it take for 15 grams of strontium to decay to 5 grams? Round answer to 2 decimal places.

Accepted Answer

A)  $40.50$ years 
B)  $450.25$ years 
C)  $45.03$ years. 
D)  $4.50$ years 
A)  $40.50$ years 
B)  $450.25$ years 
C)  $45.03$ years. 
D)  $4.50$ years

Question 17

Write the word or phrase that best completes each statement or answers the question.
-$$9 ^ { 7 x + 3 } = 27$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Find the amount that results from the investment.
-$\$ 14,000$ invested at $15 \%$ compounded semiannually after a period of 9 years

Accepted Answer

A)  $\$ 37,461.26$ 
B)  $\$ 51,461.26$ 
C)  $\$ 47,870.94$ 
D)  $\$ 49,250.27$ 
A)  $\$ 37,461.26$ 
B)  $\$ 51,461.26$ 
C)  $\$ 47,870.94$ 
D)  $\$ 49,250.27$

Question 19

Use a graphing calculator to solve the equation. Round your answer to two decimal places.
-$$\mathrm { e } ^ { \mathrm { x } } = - \mathrm { x }$$

Accepted Answer

A)  $\{ - 0.57 \}$ 
B)  $\{ 1.05 \}$ 
C)  $\{ 0.57 \}$ 
D)  $\{ - 1.05 \}$ 
A)  $\{ - 0.57 \}$ 
B)  $\{ 1.05 \}$ 
C)  $\{ 0.57 \}$ 
D)  $\{ - 1.05 \}$

Question 20

Choose the one alternative that best completes the statement or answers the question.
-The size P of a small herbivore population at time t (in years) obeys the function if they have $$\mathrm { P } ( \mathrm { t } ) = 800 \mathrm { e } ^ { 0.24 \mathrm { t } }$$ enough food and the predator population stays constant. After how many years will the population reach 1,600?

Accepted Answer

A)  8.66 yrs 
B)  27.85 yrs 
C)  7.05 yrs 
D)  2.89 yrs 
A)  8.66 yrs 
B)  27.85 yrs 
C)  7.05 yrs 
D)  2.89 yrs

The function f is one-to-one. Find its inverse. - $f ( x ) = 7 x ^ { 2 } - 8 , x \geq 0$

Solve the equation. - $\log _ { 3 } x + \log _ { 3 } ( x - 24 ) = 4$

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Use the horizontal line test to determine whether the function is one-to-one. -

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { W } \left( \frac { 13 x } { 2 } \right)$

The graph of an exponential function is given. Match the graph to one of the following functions. -

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\log _ { x } \left( \frac { 2 } { 5 } \right) = 1$

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - $f(x)=-2^{x+3}+4$ $Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f(x)=-2^{x+3}+4$

Write the word or phrase that best completes each statement or answers the question. Solve the problem. - $\text { If } \left. f ( x ) = x ^ { 2 } \text { and } g ( x ) = - 1 + 5 x \text {, find (f } g \right) ( x ) \text { and find the domain of } ( f \circ g ) ( x )$

Find a formula for the inverse of the function described below. - $32 ^ { \circ }$ Fahrenheit $= 0 ^ { \circ }$ Celsius. A function that converts temperatures in Celsius to those in Fahrenheit is $f ( x ) = \frac { 9 } { 5 } x + 32$

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - $f ( x ) = \sqrt { 2 - x } ; \quad g ( x ) = | 2 x - 1 |$

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - $f(x)=4^{(x-1)}$ $Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f(x)=4^{(x-1)}$

Approximate the value using a calculator. Express answer rounded to three decimal places. -5.52 $2.828$

Write the word or phrase that best completes each statement or answers the question. - $9 ^ { 7 x + 3 } = 27$

Find the amount that results from the investment. - $\$ 14,000$ invested at $15 \%$ compounded semiannually after a period of 9 years

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $\mathrm { e } ^ { \mathrm { x } } = - \mathrm { x }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 4: Exponential and Logarithmic Functions

The function f is one-to-one. Find its inverse. - f(x)=7x2−8,x≥0f ( x ) = 7 x ^ { 2 } - 8 , x \geq 0f(x)=7x2−8,x≥0

Use transformations to graph the function. - Use the graph of log⁡5x to obtain the graph of f(x)=−2log⁡5x. \text { Use the graph of } \log _ { 5 } x \text { to obtain the graph of } f ( x ) = - 2 \log _ { 5 } x \text {. } Use the graph of log5​x to obtain the graph of f(x)=−2log5​x.

Solve the equation. - log⁡3x+log⁡3(x−24)=4\log _ { 3 } x + \log _ { 3 } ( x - 24 ) = 4log3​x+log3​(x−24)=4