Question 1

Write in logarithmic form.
-$$2 ^ { 3 } = 8$$

Accepted Answer

A)  $\log _ { 2 } 3 = 8$ 
B)  $\log _ { 8 } 2 = 3$ 
C)  $\log _ { 2 } 8 = 3$ 
D)  $\log _ { 3 } 8 = 2$ 
A)  $\log _ { 2 } 3 = 8$ 
B)  $\log _ { 8 } 2 = 3$ 
C)  $\log _ { 2 } 8 = 3$ 
D)  $\log _ { 3 } 8 = 2$

Question 2

Decide whether the given functions are inverses.
-$$\begin{array} { l } 
f = \{ ( 2,6 ) , ( 6 , - 4 ) , ( - 4 , - 8 ) \} \
g = \{ ( 6,2 ) , ( - 4,6 ) , ( - 8,2 ) \}
\end{array}$$

Accepted Answer

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

Question 3

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-$$f ( x ) = - \sqrt { x ^ { 2 } - 25 } , x \geq 5$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { 25 - x ^ { 2 } } , x \leq 5$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 25 } , x \geq 0$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } ^ { 2 } + 25 } , \mathrm { x } \leq 0$ 
D)  $f ^ { - 1 } ( x ) = - \sqrt { 25 - x ^ { 2 } } , x \leq 0$ 
A)  $f ^ { - 1 } ( x ) = \sqrt { 25 - x ^ { 2 } } , x \leq 5$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 25 } , x \geq 0$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } ^ { 2 } + 25 } , \mathrm { x } \leq 0$ 
D)  $f ^ { - 1 } ( x ) = - \sqrt { 25 - x ^ { 2 } } , x \leq 0$

Question 4

The graph of a function f is given. Use the graph to find the indicated value.
-Let f(x) compute the cost of a rental car after x days of use at $42 per day. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

Accepted Answer

A)  The number of days rented for 42 dollars 
B)  The cost of rental for 42 days 
C)  The cost of rental for x days 
D)  The number of days rented for x dollars 
A)  The number of days rented for 42 dollars 
B)  The cost of rental for 42 days 
C)  The cost of rental for x days 
D)  The number of days rented for x dollars

Question 5

Solve the problem.
-At what interest rate must $4200 be compounded annually to equal $7521.56 after 10 yr? (Round to the nearest percent.)

Accepted Answer

A)  5% 
B)  7% 
C)  8% 
D)  6% 
A)  5% 
B)  7% 
C)  8% 
D)  6%

Question 6

Write an equivalent expression in exponential form.
-$$\log _ { 5 } x = - 2$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 25 } \right\}$ 
B)  $\left\{ \frac { 1 } { 32 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 10 \}$ 
A)  $\left\{ \frac { 1 } { 25 } \right\}$ 
B)  $\left\{ \frac { 1 } { 32 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 10 \}$

Question 7

Determine whether or not the function is one-to-one.
-$f ( x ) = \sqrt [ 3 ] { 9 x - 5 }$

Accepted Answer

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

Question 8

Choose the one alternative that best completes the statement or answers the question.
-How long will it take a sample of radioactive substance to decay to half of its original amount, if it to the nearest hundredth year.

Accepted Answer

A)  $67.60 \mathrm { yr }$ 
B)  $4.10 \mathrm { yr }$ 
C)  $35.45 \mathrm { yr }$ 
D)  $39.55 \mathrm { yr }$ 
A)  $67.60 \mathrm { yr }$ 
B)  $4.10 \mathrm { yr }$ 
C)  $35.45 \mathrm { yr }$ 
D)  $39.55 \mathrm { yr }$

Question 9

Determine whether or not the function is one-to-one.
-$$f ( x ) = \sqrt { 64 - x ^ { 2 } }$$

Accepted Answer

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

Question 10

Provide an appropriate response.
-The graph of an exponential function with base a is given. Sketch the graph of $g ( x ) = a ^ { x } + 2$. Give the domain and range of $g$.

$f(x)=a^{x}$

Accepted Answer

The answer of Provide an appropriate response.
-The graph of an...

Question 11

Choose the one alternative that best completes the statement or answers the question.
-In the formula N $\mathrm { N } = \mathrm { Ie } ^ { \mathrm { kt } }$ N is the number of items in terms of an initial population I at a given time and k is a growth constant equal to the percent of growth per unit time. There are currently 59
Million cars in a certain country, increasing by 1.2% annually. How many years will it take for this
Country to have 78 million cars? Round to the nearest year.

Accepted Answer

A)  5 yr 
B)  16 yr 
C)  245 yr 
D)  23 yr 
A)  5 yr 
B)  16 yr 
C)  245 yr 
D)  23 yr

Question 12

The graph of a function f is given. Use the graph to find the indicated value.
-$$\mathrm { f } ^ { - 1 } ( - 2 )$$

Accepted Answer

A)  5 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 3 } { 2 }$ 
D)  $- 3$ 
A)  5 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 3 } { 2 }$ 
D)  $- 3$

Question 13

Use the change of base rule to find the logarithm to four decimal places.
-$$\log _ { 3 } 5$$

Accepted Answer

A)  2.9300 
B)  1.4650 
C)  0.6826 
D)  -1.4650 
A)  2.9300 
B)  1.4650 
C)  0.6826 
D)  -1.4650

Question 14

Graph the function.
-$f(x)=4^{x}$

Accepted Answer

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

Question 15

Write the word or phrase that best completes each statement or answers the question.
-Why does logaa always equal 1 for any valid base a?

Accepted Answer

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

Question 16

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $$a \neq 1 \text { and } b \neq 1$$
-$\left( \log _ { a } m - \log _ { a } n \right) + 3 \log _ { a } k$

Accepted Answer

A)  $\log _ { a } \left( \frac { m ^ { 3 } } { n } \right)$ 
B)  $\log _ { a } \left( \frac { m } { k ^ { 3 } n } \right)$ 
C)  $\log _ { a } \left( m + k ^ { 3 } - n \right)$ 
D)  $\log _ { a } \left( \frac { 3 m k } { n } \right)$ 
A)  $\log _ { a } \left( \frac { m ^ { 3 } } { n } \right)$ 
B)  $\log _ { a } \left( \frac { m } { k ^ { 3 } n } \right)$ 
C)  $\log _ { a } \left( m + k ^ { 3 } - n \right)$ 
D)  $\log _ { a } \left( \frac { 3 m k } { n } \right)$

Question 17

Choose the one alternative that best completes the statement or answers the question.
-A population is increasing according to the exponential function defined by $y = 3 \mathrm { e } ^ { 04 x }$, where $y$ is in millions and $x$ is the number of years. Which of the following should be done in order to answer the question "How large will the population be in 3 months?"

Accepted Answer

A)  Evaluate $y = 3 e ^ { - 04 ( 1 / 4 ) }$. 
B)  Solve $3 e ^ { \cdot 04 x } = 1 / 4$. 
C)  Evaluate $y = 3 e ^ { \cdot 04 ( 3 ) }$. 
D)  Solve $3 \mathrm { e } ^ { \cdot 04 \mathrm { x } } = 3$. 
A)  Evaluate $y = 3 e ^ { - 04 ( 1 / 4 ) }$. 
B)  Solve $3 e ^ { \cdot 04 x } = 1 / 4$. 
C)  Evaluate $y = 3 e ^ { \cdot 04 ( 3 ) }$. 
D)  Solve $3 \mathrm { e } ^ { \cdot 04 \mathrm { x } } = 3$.

Question 18

Determine whether or not the function is one-to-one.
-$$f ( x ) = \sqrt { x + 7 }$$

Accepted Answer

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

Question 19

Find the domain and range of the inverse of the given function.
-$$f ( x ) = - \frac { 3 } { x }$$

Accepted Answer

A)  Domain and range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: all real numbers; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: all real numbers 
D)  Domain and range: all real numbers 
A)  Domain and range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: all real numbers; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: all real numbers 
D)  Domain and range: all real numbers

Question 20

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent
positive real numbers.
-$\log _ { 3 } ( 10 x + 8 y )$

Accepted Answer

A)  $\log _ { 3 } 10 x + \log _ { 3 } 8 y$ 
B)  $\log _ { 3 } ( 10 x + 8 y )$ 
C)  $\log _ { 3 } 80 x y$ 
D)  $\left( \log _ { 3 } 10 x \right) \left( \log _ { 3 } 8 y \right)$ 
A)  $\log _ { 3 } 10 x + \log _ { 3 } 8 y$ 
B)  $\log _ { 3 } ( 10 x + 8 y )$ 
C)  $\log _ { 3 } 80 x y$ 
D)  $\left( \log _ { 3 } 10 x \right) \left( \log _ { 3 } 8 y \right)$

Write in logarithmic form. - $2 ^ { 3 } = 8$

Decide whether the given functions are inverses. - f=\{(2,6),(6,-4),(-4,-8)\} g=\{(6,2),(-4,6),(-8,2)\}

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = - \sqrt { x ^ { 2 } - 25 } , x \geq 5$

The graph of a function f is given. Use the graph to find the indicated value. -Let f(x) compute the cost of a rental car after x days of use at $42 per day. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

Solve the problem. -At what interest rate must $4200 be compounded annually to equal $7521.56 after 10 yr? (Round to the nearest percent.)

Write an equivalent expression in exponential form. - $\log _ { 5 } x = - 2$

Determine whether or not the function is one-to-one. - $f ( x ) = \sqrt [ 3 ] { 9 x - 5 }$

Choose the one alternative that best completes the statement or answers the question. -How long will it take a sample of radioactive substance to decay to half of its original amount, if it to the nearest hundredth year.

Determine whether or not the function is one-to-one. - $f ( x ) = \sqrt { 64 - x ^ { 2 } }$

The graph of a function f is given. Use the graph to find the indicated value. - $\mathrm { f } ^ { - 1 } ( - 2 )$ $The graph of a function f is given. Use the graph to find the indicated value. - \mathrm { f } ^ { - 1 } ( - 2 )$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 3 } 5$

Graph the function. - $f(x)=4^{x}$ $Graph the function. - f(x)=4^{x}$

Write the word or phrase that best completes each statement or answers the question. -Why does logaa always equal 1 for any valid base a?

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ - $\left( \log _ { a } m - \log _ { a } n \right) + 3 \log _ { a } k$

Determine whether or not the function is one-to-one. - $f ( x ) = \sqrt { x + 7 }$

Find the domain and range of the inverse of the given function. - $f ( x ) = - \frac { 3 } { x }$

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { 3 } ( 10 x + 8 y )$

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

Write in logarithmic form. - 23=82 ^ { 3 } = 823=8