Question 1

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-2 - x = 5-x

Accepted Answer

A)  {3.06} 
B)  {1.86} 
C)  {2.06} 
D)  {-0.59, 1.96} 
A)  {3.06} 
B)  {1.86} 
C)  {2.06} 
D)  {-0.59, 1.96} D

Question 2

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$f ( x ) = 4 x + 8$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 8 } { 4 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 8 } { 4 }$ 
C)  not a one-to-one 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 } - 8$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 8 } { 4 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 8 } { 4 }$ 
C)  not a one-to-one 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 } - 8$ B

Question 3

Find the value. Give an approximation to four decimal places.
-$\log 0.0963$

Accepted Answer

A)  $- 1.0119$ 
B)  $- 1.0164$ 
C)  $- 1.0209$ 
D)  $- 2.3403$ 
A)  $- 1.0119$ 
B)  $- 1.0164$ 
C)  $- 1.0209$ 
D)  $- 2.3403$ B

Question 4

Write the word or phrase that best completes each statement or answers the question.
-The purchasing power of a dollar is decreasing at the rate of $3.5 \%$ annually, compounded continuously. How long will it take for the purchasing power of $\$ 1.00$ to be worth $\$ 0.62$ ? Round answers to the nearest hundredth.

Accepted Answer

A)  $1.37 \mathrm { yr }$ 
B)  $17.71 \mathrm { yr }$ 
C)  $13.66 \mathrm { yr }$ 
D)  $0.14 \mathrm { yr }$ 
A)  $1.37 \mathrm { yr }$ 
B)  $17.71 \mathrm { yr }$ 
C)  $13.66 \mathrm { yr }$ 
D)  $0.14 \mathrm { yr }$

Question 5

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$\mathrm { x } ^ { 2 } + 6 \mathrm { x } + 3 = \mathrm { e } ^ { \mathrm { x } - 1 } + 2$$

Accepted Answer

A)  $\{ - 5.81 , - 0.16 \}$ 
B)  $\{ - 5.83 , - 0.11 \}$ 
C)  $\{ - 5.85 , - 0.12 \}$ 
D)  $\{ - 5.03 \}$ 
A)  $\{ - 5.81 , - 0.16 \}$ 
B)  $\{ - 5.83 , - 0.11 \}$ 
C)  $\{ - 5.85 , - 0.12 \}$ 
D)  $\{ - 5.03 \}$

Question 6

Graph the exponential function using transformations where appropriate.
-$f(x)=3^{x}+5$

Accepted Answer

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

Question 7

Determine whether the statement is true or false.
-If f is a one-to-one function and the graph of f lies completely within the third quadrant, then the
graph of $$\mathrm { f } ^{- 1}$$ lies completely within the third quadrant.

Accepted Answer

A) True 
 B)False

Question 8

Solve the equation. Round to the nearest thousandth.
-$$3 ( x + 7 ) = 6 ^ { x }$$

Accepted Answer

A)  $\{ 12.655 \}$ 
B)  $\{ 11.095 \}$ 
C)  $\{ 9.535 \}$ 
D)  $\{ - 11.095 \}$ 
A)  $\{ 12.655 \}$ 
B)  $\{ 11.095 \}$ 
C)  $\{ 9.535 \}$ 
D)  $\{ - 11.095 \}$

Question 9

Write an equation for the graph given. The graph represents an exponential function f with base 2 or 3, translated and/or reflected.
-

Accepted Answer

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

Question 10

Write in logarithmic form.
-$$10 ^ { 2 } = 100$$

Accepted Answer

A)  $\log _ { 2 } 100 = 10$ 
B)  $\log _ { 10 } 100 = 2$ 
C)  $\log _ { 10 } 2 = 100$ 
D)  $\log _ { 2 } 10 = 100$ 
A)  $\log _ { 2 } 100 = 10$ 
B)  $\log _ { 10 } 100 = 2$ 
C)  $\log _ { 10 } 2 = 100$ 
D)  $\log _ { 2 } 10 = 100$

Question 11

Solve the problem.
-The growth in population of a city can be seen using the formula $p ( t ) = 6680 \mathrm { e } ^ { 0.004 t }$, where $t$ is the number of years. According to this formula, in how many years will the population reach 10,020 ? Round to the nearest tenth of a year.

Accepted Answer

A)  $50.7 \mathrm { yr }$ 
B)  $76.0 \mathrm { yr }$ 
C)  $202.7 \mathrm { yr }$ 
D)  $101.4 \mathrm { yr }$ 
A)  $50.7 \mathrm { yr }$ 
B)  $76.0 \mathrm { yr }$ 
C)  $202.7 \mathrm { yr }$ 
D)  $101.4 \mathrm { yr }$

Question 12

Solve the equation. Round to the nearest thousandth.
-$$2 ( 5 x - 3 ) = 16$$

Accepted Answer

A)  $\{ 1.016 \}$ 
B)  $\{ 1.400 \}$ 
C)  $\{ 0.200 \}$ 
D)  $\{ 2.200 \}$ 
A)  $\{ 1.016 \}$ 
B)  $\{ 1.400 \}$ 
C)  $\{ 0.200 \}$ 
D)  $\{ 2.200 \}$

Question 13

Match the function with its graph.
-$$f ( x ) = \log _ { 5 } ( - x )$$

Accepted Answer

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

Question 14

Find the future value.
-$59,981 invested for 3 years at 6% compounded semiannually

Accepted Answer

A)  $71,438.33 
B)  $71,778.09 
C)  $71,620.45 
D)  $71,714.37 
A)  $71,438.33 
B)  $71,778.09 
C)  $71,620.45 
D)  $71,714.37

Question 15

Graph the exponential function using transformations where appropriate.
-$f(x)=\left(\frac{1}{2}\right)^{x}-3$

Accepted Answer

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

Question 16

Solve the problem.
-An element decays at the rate of S(t) = se-0.038t, where s is the initial amount in grams and t is the time in years since this initial amount was present. If you have a 30-gram piece of this
Element, how many grams will you have 2 years from now? Round your answer to the nearest
Tenth of a gram.

Accepted Answer

A)  0.9 g 
B)  32.4 g 
C)  14.4 g 
D)  27.8 g 
A)  0.9 g 
B)  32.4 g 
C)  14.4 g 
D)  27.8 g

Question 17

Write the word or phrase that best completes each statement or answers the question.
-$$\text { Explain why } \mathrm { a } ^ { \log _ { \mathrm { a } } 5 } = 5 \text {. }$$

Accepted Answer

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

Question 18

Solve the equation.
-$$2 ^ { - x } = \frac { 1 } { 16 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 8 } \right\}$ 
B)  $\left\{ \frac { 1 } { 4 } \right\}$ 
C)  $\{ 4 \}$ 
D)  $\{ - 4 \}$ 
A)  $\left\{ \frac { 1 } { 8 } \right\}$ 
B)  $\left\{ \frac { 1 } { 4 } \right\}$ 
C)  $\{ 4 \}$ 
D)  $\{ - 4 \}$

Question 19

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected.
-

Accepted Answer

A)  $\log _ { 3 } ( - x - 8 )$ 
B)  $- \log _ { 3 } ( x - 8 )$ 
C)  $- \log _ { 3 } ( - x + 8 )$ 
D)  $- \log _ { 3 } ( x + 8 )$ 
A)  $\log _ { 3 } ( - x - 8 )$ 
B)  $- \log _ { 3 } ( x - 8 )$ 
C)  $- \log _ { 3 } ( - x + 8 )$ 
D)  $- \log _ { 3 } ( x + 8 )$

Question 20

Solve the problem.
-Suppose the government wants to impose a tax on fossil fuels to reduce carbon emissions. The cost benefit is modeled by $\ln ( 1 - \mathrm { P } ) = - 0.0025 - 0.0058 \mathrm { x }$, where $x$ represents the dollars of tax per ton of carbon emitted and $\mathrm { P }$ represents the percent reduction in emissions of carbon. ( $\mathrm { P }$ is in decimal form.) Determine $\mathrm { P }$ when $\mathrm { x } = 70$. Round to three decimal places.

Accepted Answer

A)  $- 0.17$ 
B)  $- 0.332$ 
C)  $1.665$ 
D)  $0.335$ 
A)  $- 0.17$ 
B)  $- 0.332$ 
C)  $1.665$ 
D)  $0.335$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. -2 - x = 5-x

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $f ( x ) = 4 x + 8$

Find the value. Give an approximation to four decimal places. - $\log 0.0963$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { x } ^ { 2 } + 6 \mathrm { x } + 3 = \mathrm { e } ^ { \mathrm { x } - 1 } + 2$

Graph the exponential function using transformations where appropriate. - $f(x)=3^{x}+5$ $Graph the exponential function using transformations where appropriate. - f(x)=3^{x}+5$

Determine whether the statement is true or false. -If f is a one-to-one function and the graph of f lies completely within the third quadrant, then the graph of $\mathrm { f } ^{- 1}$ lies completely within the third quadrant.

Solve the equation. Round to the nearest thousandth. - $3 ( x + 7 ) = 6 ^ { x }$

Write an equation for the graph given. The graph represents an exponential function f with base 2 or 3, translated and/or reflected. -

Write in logarithmic form. - $10 ^ { 2 } = 100$

Solve the problem. -The growth in population of a city can be seen using the formula $p ( t ) = 6680 \mathrm { e } ^ { 0.004 t }$ , where $t$ is the number of years. According to this formula, in how many years will the population reach 10,020 ? Round to the nearest tenth of a year.

Solve the equation. Round to the nearest thousandth. - $2 ( 5 x - 3 ) = 16$

Match the function with its graph. - $f ( x ) = \log _ { 5 } ( - x )$

Find the future value. -$59,981 invested for 3 years at 6% compounded semiannually

Graph the exponential function using transformations where appropriate. - $f(x)=\left(\frac{1}{2}\right)^{x}-3$ $Graph the exponential function using transformations where appropriate. - f(x)=\left(\frac{1}{2}\right)^{x}-3$

Write the word or phrase that best completes each statement or answers the question. - $\text { Explain why } \mathrm { a } ^ { \log _ { \mathrm { a } } 5 } = 5 \text {. }$

Solve the equation. - $2 ^ { - x } = \frac { 1 } { 16 }$

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 4: Inverse, Exponential, and Logarithmic Functions

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. -2 - x = 5-x

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - f(x)=4x+8f ( x ) = 4 x + 8f(x)=4x+8

Find the value. Give an approximation to four decimal places. - log⁡0.0963\log 0.0963log0.0963

Solve the following graphically. If necessary, round answers to the nearest thousandth. - x2+6x+3=ex−1+2\mathrm { x } ^ { 2 } + 6 \mathrm { x } + 3 = \mathrm { e } ^ { \mathrm { x } - 1 } + 2x2+6x+3=ex−1+2

Graph the exponential function using transformations where appropriate. - f(x)=3x+5f(x)=3^{x}+5f(x)=3x+5

Determine whether the statement is true or false. -If f is a one-to-one function and the graph of f lies completely within the third quadrant, then the graph of f−1\mathrm { f } ^{- 1}f−1 lies completely within the third quadrant.

Solve the equation. Round to the nearest thousandth. - 3(x+7)=6x3 ( x + 7 ) = 6 ^ { x }3(x+7)=6x

Write an equation for the graph given. The graph represents an exponential function f with base 2 or 3, translated and/or reflected. -

Write in logarithmic form. - 102=10010 ^ { 2 } = 100102=100

Solve the equation. Round to the nearest thousandth. - 2(5x−3)=162 ( 5 x - 3 ) = 162(5x−3)=16

Match the function with its graph. - f(x)=log⁡5(−x)f ( x ) = \log _ { 5 } ( - x )f(x)=log5​(−x)

Find the future value. -$59,981 invested for 3 years at 6% compounded semiannually

Graph the exponential function using transformations where appropriate. - f(x)=(12)x−3f(x)=\left(\frac{1}{2}\right)^{x}-3f(x)=(21​)x−3

Write the word or phrase that best completes each statement or answers the question. - Explain why alog⁡a5=5. \text { Explain why } \mathrm { a } ^ { \log _ { \mathrm { a } } 5 } = 5 \text {. } Explain why aloga​5=5.

Solve the equation. - 2−x=1162 ^ { - x } = \frac { 1 } { 16 }2−x=161​

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $f ( x ) = 4 x + 8$

Find the value. Give an approximation to four decimal places. - $\log 0.0963$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { x } ^ { 2 } + 6 \mathrm { x } + 3 = \mathrm { e } ^ { \mathrm { x } - 1 } + 2$

Graph the exponential function using transformations where appropriate. - $f(x)=3^{x}+5$ $Graph the exponential function using transformations where appropriate. - f(x)=3^{x}+5$

Determine whether the statement is true or false. -If f is a one-to-one function and the graph of f lies completely within the third quadrant, then the graph of $\mathrm { f } ^{- 1}$ lies completely within the third quadrant.

Solve the equation. Round to the nearest thousandth. - $3 ( x + 7 ) = 6 ^ { x }$

Write in logarithmic form. - $10 ^ { 2 } = 100$

Solve the equation. Round to the nearest thousandth. - $2 ( 5 x - 3 ) = 16$

Match the function with its graph. - $f ( x ) = \log _ { 5 } ( - x )$

Graph the exponential function using transformations where appropriate. - $f(x)=\left(\frac{1}{2}\right)^{x}-3$ $Graph the exponential function using transformations where appropriate. - f(x)=\left(\frac{1}{2}\right)^{x}-3$

Write the word or phrase that best completes each statement or answers the question. - $\text { Explain why } \mathrm { a } ^ { \log _ { \mathrm { a } } 5 } = 5 \text {. }$

Solve the equation. - $2 ^ { - x } = \frac { 1 } { 16 }$