Question 1

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-{(3, -5), (5, -3), (9, 2), (-9, -2)} 49)

Accepted Answer

A)  {(-2, 9), (9, 5), (-5, 3), (2, -9)} 
B)  {(-5, 3), (-3, 5), (2, 9), (-2, -9)} 
C)  not one-to-one 
D)  {(-2, 9), (-3, 5), (-5, 5), (2, -9)} 
A)  {(-2, 9), (9, 5), (-5, 3), (2, -9)} 
B)  {(-5, 3), (-3, 5), (2, 9), (-2, -9)} 
C)  not one-to-one 
D)  {(-2, 9), (-3, 5), (-5, 5), (2, -9)}

Question 2

Graph the exponential function using transformations where appropriate.
-$$\begin{array} { l } 
f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } - 4 \

\end{array}$$

Accepted Answer

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

Question 3

Use the change of base rule to find the logarithm to four decimal places.
-$$\log _ { 3 } 0.68$$

Accepted Answer

A)  -0.3510 
B)  -0.7020 
C)  0.3510 
D)  -2.8486 
A)  -0.3510 
B)  -0.7020 
C)  0.3510 
D)  -2.8486

Question 4

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$2 ( 4 x - 1 ) = 12$$

Accepted Answer

A)  $\{ 0.93 \}$ 
B)  $\{ 1.15 \}$ 
C)  $\{ 1.75 \}$ 
D)  $\{ 0.65 \}$ 
A)  $\{ 0.93 \}$ 
B)  $\{ 1.15 \}$ 
C)  $\{ 1.75 \}$ 
D)  $\{ 0.65 \}$

Question 5

Write the word or phrase that best completes each statement or answers the question.
-Explain the error in the following: $\log _ { 6 } 8 - \log _ { 6 } N = \log _ { 6 } ( 8 - N )$

Accepted Answer

A difference of logarithms is

Question 6

Write an equivalent expression in exponential form.
-$$\log _ { 1 / 3 } ( x + 3 ) = - 3$$

Accepted Answer

A)  30 
B)  27 
C)  36 
D)  24 
A)  30 
B)  27 
C)  36 
D)  24

Question 7

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $$a \neq 1 \text { and } b \neq 1$$
-$6 \log _ { a } q - 3 \log _ { a } p ^ { 2 }$

Accepted Answer

A)  $\log _ { a } \left( \frac { q ^ { 6 } } { p ^ { 6 } } \right)$ 
B)  $\frac { \log _ { a } q ^ { 6 } } { \log _ { a } p ^ { 6 } }$ 
C)  $\log _ { a } \left( \frac { q ^ { 6 } } { p ^ { 5 } } \right)$ 
D)  $\log _ { a } \left( \frac { 6 q } { 3 p ^ { 2 } } \right)$ 
A)  $\log _ { a } \left( \frac { q ^ { 6 } } { p ^ { 6 } } \right)$ 
B)  $\frac { \log _ { a } q ^ { 6 } } { \log _ { a } p ^ { 6 } }$ 
C)  $\log _ { a } \left( \frac { q ^ { 6 } } { p ^ { 5 } } \right)$ 
D)  $\log _ { a } \left( \frac { 6 q } { 3 p ^ { 2 } } \right)$

Question 8

Choose the one alternative that best completes the statement or answers the question.
-Assume the cost of a gallon of milk is $\$ 3.00$. With continuous compounding, find the time it would take the cost to be 4 times as much (to the nearest tenth of a year), at an annual inflation rate of $6 \%$.

Accepted Answer

A)  $23.1 \mathrm { yr }$ 
B)  $0.1 \mathrm { yr }$ 
C)  $0.0 \mathrm { yr }$ 
D)  $8.5 \mathrm { yr }$ 
A)  $23.1 \mathrm { yr }$ 
B)  $0.1 \mathrm { yr }$ 
C)  $0.0 \mathrm { yr }$ 
D)  $8.5 \mathrm { yr }$

Question 9

Solve the problem.
-Use your graphing calculator to find how long it will take for $8500 invested at 4.825% per year compounded daily to triple in value. Find the answer to the nearest year. Use 365 days for a year.

Accepted Answer

A)  0 yr 
B)  23 yr 
C)  3,033,623 yr 
D)  30,534 yr 
A)  0 yr 
B)  23 yr 
C)  3,033,623 yr 
D)  30,534 yr

Question 10

Find the value. Give an approximation to four decimal places.
-$\log \left( 7.75 \times 10 ^ { 4 } \right)$

Accepted Answer

A)  $4.8893$ 
B)  $- 3.1107$ 
C)  $0.8893$ 
D)  $4.0003$ 
A)  $4.8893$ 
B)  $- 3.1107$ 
C)  $0.8893$ 
D)  $4.0003$

Question 11

Evaluate the logarithm.
-$\log _ { 10 } 0.1$

Accepted Answer

A)  $- 0.1$ 
B)  $0.1$ 
C)  1 
D)  $- 1$ 
A)  $- 0.1$ 
B)  $0.1$ 
C)  1 
D)  $- 1$

Question 12

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent
positive real numbers.
-$\log \sqrt { \frac { 4 x ^ { 5 } } { z ^ { 3 } } }$

Accepted Answer

A)  $\sqrt { \log _ { b } 4 } + \sqrt { \log _ { b } x ^ { 5 } } - \sqrt { \log _ { b } z ^ { 3 } }$ 
B)  $\log _ { b } 2 + \frac { 5 } { 2 } \log _ { b } x - \frac { 3 } { 2 } \log b z$ 
C)  $\log _ { b } 2 \cdot \frac { 5 } { 2 } \log _ { b } x - \frac { 3 } { 2 } \log _ { b } z$ 
D)  $\left( \log _ { b } 2 + + \frac { 5 } { 2 } \log _ { b } x \right) \div \frac { 3 } { 2 } \log _ { b } z$ 
A)  $\sqrt { \log _ { b } 4 } + \sqrt { \log _ { b } x ^ { 5 } } - \sqrt { \log _ { b } z ^ { 3 } }$ 
B)  $\log _ { b } 2 + \frac { 5 } { 2 } \log _ { b } x - \frac { 3 } { 2 } \log b z$ 
C)  $\log _ { b } 2 \cdot \frac { 5 } { 2 } \log _ { b } x - \frac { 3 } { 2 } \log _ { b } z$ 
D)  $\left( \log _ { b } 2 + + \frac { 5 } { 2 } \log _ { b } x \right) \div \frac { 3 } { 2 } \log _ { b } z$

Question 13

Explain how the graph of can be obtained from the graph o
-What is the domain of the function $y = \log _ { 7 } x ?$

Accepted Answer

A)  $( 0 , \infty )$ 
B)  $( \infty , \infty )$ 
C)  $[ 0 , \infty )$ 
D)  $( 7 , \infty )$ 
A)  $( 0 , \infty )$ 
B)  $( \infty , \infty )$ 
C)  $[ 0 , \infty )$ 
D)  $( 7 , \infty )$

Question 14

Evaluate the logarithm.
-$$\log _ { 9 } \frac { 1 } { 81 }$$

Accepted Answer

A)  9 
B)  $- 9$ 
C)  $- 2$ 
D)  2 
A)  9 
B)  $- 9$ 
C)  $- 2$ 
D)  2

Question 15

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

Question 16

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function
is one-to-one. If the function is one-to-one, give the equation of the inverse function.
-$$f ( x ) = \frac { - x } { x + 2 } ; [ - 8,8 ] \text { by } [ - 8,8 ]$$

Accepted Answer

A)  one-to-one; $f ^ { - 1 } ( x ) = \frac { - 2 x } { x + 1 }$ 
B)  not one-to-one 
C)  one-to-one; $f ^ { - 1 } ( x ) = \frac { 2 x } { x + 1 }$ 
D)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } } { \mathrm { x } + 2 }$ 
A)  one-to-one; $f ^ { - 1 } ( x ) = \frac { - 2 x } { x + 1 }$ 
B)  not one-to-one 
C)  one-to-one; $f ^ { - 1 } ( x ) = \frac { 2 x } { x + 1 }$ 
D)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } } { \mathrm { x } + 2 }$

Question 17

Graph the function. Give the domain and range.
-$$\begin{array} { l } 
\mathrm { f } ( \mathrm { x } ) = \log _ { 2 } ( \mathrm { x } + 2 ) \

\end{array}$$

Accepted Answer

A)  domain: $( - 2 , \infty )$; range: $( \infty , \infty )$
  
B)  domain: $( \infty , \infty )$; range: $( 2 , \infty )$
  
C)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
D)  domain: $( \infty , \infty )$; range: $( 0 , \infty )$
  
A)  domain: $( - 2 , \infty )$; range: $( \infty , \infty )$
  
B)  domain: $( \infty , \infty )$; range: $( 2 , \infty )$
  
C)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
D)  domain: $( \infty , \infty )$; range: $( 0 , \infty )$

Question 18

Decide whether the pair of functions graphed are inverses.
-

Accepted Answer

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

Question 19

Use the graph of f to sketch a graph of the inverse of f using a dashed curve.
-

Accepted Answer

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

Question 20

Write the word or phrase that best completes each statement or answers the question.
-The graph of $\mathrm { y } = \mathrm { e } ^ { \mathrm { x } }$ is shown with the coordinates of a point displayed at the bottom of the screen. Write the logarithmic equation associated with the display.

Accepted Answer

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

If the function is one-to-one, find its inverse. If not, write "not one-to-one." -{(3, -5), (5, -3), (9, 2), (-9, -2)} 49)

Graph the exponential function using transformations where appropriate. - f(x)=-4 $Graph the exponential function using transformations where appropriate. - \begin{array} { l } f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } - 4 \\ \end{array}$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 3 } 0.68$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 ( 4 x - 1 ) = 12$

Write the word or phrase that best completes each statement or answers the question. -Explain the error in the following: $\log _ { 6 } 8 - \log _ { 6 } N = \log _ { 6 } ( 8 - N )$

Write an equivalent expression in exponential form. - $\log _ { 1 / 3 } ( x + 3 ) = - 3$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ - $6 \log _ { a } q - 3 \log _ { a } p ^ { 2 }$

Choose the one alternative that best completes the statement or answers the question. -Assume the cost of a gallon of milk is $\$ 3.00$ . With continuous compounding, find the time it would take the cost to be 4 times as much (to the nearest tenth of a year), at an annual inflation rate of $6 \%$ .

Solve the problem. -Use your graphing calculator to find how long it will take for $8500 invested at 4.825% per year compounded daily to triple in value. Find the answer to the nearest year. Use 365 days for a year.

Find the value. Give an approximation to four decimal places. - $\log \left( 7.75 \times 10 ^ { 4 } \right)$

Evaluate the logarithm. - $\log _ { 10 } 0.1$

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log \sqrt { \frac { 4 x ^ { 5 } } { z ^ { 3 } } }$

Explain how the graph of can be obtained from the graph o -What is the domain of the function $y = \log _ { 7 } x ?$

Evaluate the logarithm. - $\log _ { 9 } \frac { 1 } { 81 }$

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

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function. - $f ( x ) = \frac { - x } { x + 2 } ; [ - 8,8 ] \text { by } [ - 8,8 ]$

Graph the function. Give the domain and range. - ()=(+2) $Graph the function. Give the domain and range. - \begin{array} { l } \mathrm { f } ( \mathrm { x } ) = \log _ { 2 } ( \mathrm { x } + 2 ) \\ \end{array}$

Decide whether the pair of functions graphed are inverses. -

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Review of Basic Concepts

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

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

If the function is one-to-one, find its inverse. If not, write "not one-to-one." -{(3, -5), (5, -3), (9, 2), (-9, -2)} 49)

Graph the exponential function using transformations where appropriate. - f(x)=-4

Use the change of base rule to find the logarithm to four decimal places. - log⁡30.68\log _ { 3 } 0.68log3​0.68

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 2(4x−1)=122 ( 4 x - 1 ) = 122(4x−1)=12

Write the word or phrase that best completes each statement or answers the question. -Explain the error in the following: log⁡68−log⁡6N=log⁡6(8−N)\log _ { 6 } 8 - \log _ { 6 } N = \log _ { 6 } ( 8 - N )log6​8−log6​N=log6​(8−N)

Write an equivalent expression in exponential form. - log⁡1/3(x+3)=−3\log _ { 1 / 3 } ( x + 3 ) = - 3log1/3​(x+3)=−3

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with a≠1 and b≠1a \neq 1 \text { and } b \neq 1a=1 and b=1 - 6log⁡aq−3log⁡ap26 \log _ { a } q - 3 \log _ { a } p ^ { 2 }6loga​q−3loga​p2