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)}

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)

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

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)  $\{ 0.65 \}$

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

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

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

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)  $\log _ { a } \left( \frac { 6 q } { 3 p ^ { 2 } } \right)$

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)  $8.5 \mathrm { yr }$

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

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)  $4.0003$

Question 11

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

Accepted Answer

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)  $\left( \log _ { b } 2 + + \frac { 5 } { 2 } \log _ { b } x \right) \div \frac { 3 } { 2 } \log _ { b } z$

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)  $( 7 , \infty )$

Question 14

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

Accepted Answer

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)  $- 2 ^ { x + 2 } + 2$

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; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } } { \mathrm { x } + 2 }$

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: $( 0 , \infty )$

Question 18

Decide whether the pair of functions graphed are inverses.
-

Accepted Answer

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)

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...

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)

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

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. - $f ( x ) = \frac { - x } { x + 2 } ; [ - 8,8 ] \text { by } [ - 8,8 ]$

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. -

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) =(12) x−4\begin{array} { l } f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } - 4 \\\end{array}f(x) =(21​) 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

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⁡(7.75×104) \log \left( 7.75 \times 10 ^ { 4 } \right) log(7.75×104)

Evaluate the logarithm. - log⁡100.1\log _ { 10 } 0.1log10​0.1

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - log⁡4x5z3\log \sqrt { \frac { 4 x ^ { 5 } } { z ^ { 3 } } }logz34x5​​

Explain how the graph of can be obtained from the graph o -What is the domain of the function y=log⁡7x?y = \log _ { 7 } x ?y=log7​x?

Evaluate the logarithm. - log⁡9181\log _ { 9 } \frac { 1 } { 81 }log9​811​

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

Graph the function. Give the domain and range. - f(x) =log⁡2(x+2) \begin{array} { l } \mathrm { f } ( \mathrm { x } ) = \log _ { 2 } ( \mathrm { x } + 2 ) \\\end{array}f(x) =log2​(x+2) ​