Question 1

Find the domain of the function.
-$$f ( x ) = \log _ { 9 } ( x + 8 ) ^ { 2 }$$

Accepted Answer

A)  $( - \infty , 0 )$ or $( 0 , \infty )$ 
B)  $( - 8 , \infty )$ 
C)  $( - \infty , - 8 )$ or $( - 8 , \infty )$ 
D)  $( 8 , \infty )$ 
A)  $( - \infty , 0 )$ or $( 0 , \infty )$ 
B)  $( - 8 , \infty )$ 
C)  $( - \infty , - 8 )$ or $( - 8 , \infty )$ 
D)  $( 8 , \infty )$

Question 2

Evaluate the expression using the values given in the table.
-$$\begin{array}{l}
( g f ) ( 1 )\
\begin{array} { c | r | r | r | r } 
x & 1 & 6 & 10 & 12 \
\hline f ( x ) & - 2 & 10 & 3 & 12
\end{array}\
\begin{array} { c | r | r | r | r } 
\mathrm { x } & - 5 & - 2 & 1 & 3 \
\hline \mathrm { g } ( \mathrm { x } ) & 1 & - 5 & 6 & 10
\end{array}
\end{array}$$

Accepted Answer

A)  10 
B)  -2 
C)  6 
D)  -5 
A)  10 
B)  -2 
C)  6 
D)  -5

Question 3

For the given functions f and g, find the requested composite function.
-$f ( x ) = 4 x ^ { 2 } + 6 x + 3 , \quad g ( x ) = 6 x - 7 ; \quad$ Find $( g \circ f ) ( x )$

Accepted Answer

A)  $4 x ^ { 2 } + 36 x + 11$ 
B)  $24 x ^ { 2 } + 36 x + 25$ 
C)  $4 x ^ { 2 } + 6 x - 4$ 
D)  $24 x ^ { 2 } + 36 x + 11$ 
A)  $4 x ^ { 2 } + 36 x + 11$ 
B)  $24 x ^ { 2 } + 36 x + 25$ 
C)  $4 x ^ { 2 } + 6 x - 4$ 
D)  $24 x ^ { 2 } + 36 x + 11$

Question 4

Solve the problem.
-In a networking marketing plan for a company, each distributor is expected to recruit 3 new distributors. Jack
was the first distributor hired by the company, so he is considered a level 1 distributor. The 3 people he recruits
are considered level 2 distributors. The people recruited by the level 2 distributors are considered level 3
distributors, and so on. Write a function that models the number of distributors D at each level L. How many
distributors would there be at the fifth level?

Accepted Answer

The answer of Solve the problem.
-In a networking marketing plan...

Question 5

Solve the problem.
-The half-life of silicon-32 is 710 years. If 10 grams is present now, how much will be present in 800 years? (Round your answer to three decimal places.)

Accepted Answer

A)  0.004 
B)  9.249 
C)  4.579 
D)  0 
A)  0.004 
B)  9.249 
C)  4.579 
D)  0

Question 6

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of
the inverse.
-$$f ( x ) = \frac { 4 } { 6 x + 5 }$$

Accepted Answer

A)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 2 } { 3 } \right\} , R = \left\{ y \mid y \neq \frac { 4 } { 5 } \right\}$;
 $f ^ { - 1 } ( x ) : D = \left\{ x \mid x \neq \frac { 4 } { 5 } \right\} , R = \left\{ y \mid y \neq \frac { 2 } { 3 } \right\}$ 
B)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 5 } { 6 } \right\} R = \{ y \mid y \neq - 5 \}$; 
$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } | \mathrm { x } \neq - 5 \rangle , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 5 } { 6 } \right\} \right.$ 
C)  $f ( x )$ : $D$ is all real numbers, $R$ is all real number:
$\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ : $\mathrm { D }$ is all real numbers, $R$ is all real numbe 
D)  $f ( x ) : D = \left\{ x \mid x \neq - \frac { 5 } { 6 } \right\} , R = \{ y \mid y \neq 0 \}$
$$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq 0 \} , \mathrm { R } = \left\{ \mathrm { y } \mid \mathrm { y } \neq - \frac { 5 } { 6 } \right\}$$ ; 
A)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 2 } { 3 } \right\} , R = \left\{ y \mid y \neq \frac { 4 } { 5 } \right\}$;
 $f ^ { - 1 } ( x ) : D = \left\{ x \mid x \neq \frac { 4 } { 5 } \right\} , R = \left\{ y \mid y \neq \frac { 2 } { 3 } \right\}$ 
B)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 5 } { 6 } \right\} R = \{ y \mid y \neq - 5 \}$; 
$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } | \mathrm { x } \neq - 5 \rangle , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 5 } { 6 } \right\} \right.$ 
C)  $f ( x )$ : $D$ is all real numbers, $R$ is all real number:
$\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ : $\mathrm { D }$ is all real numbers, $R$ is all real numbe 
D)  $f ( x ) : D = \left\{ x \mid x \neq - \frac { 5 } { 6 } \right\} , R = \{ y \mid y \neq 0 \}$
$$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq 0 \} , \mathrm { R } = \left\{ \mathrm { y } \mid \mathrm { y } \neq - \frac { 5 } { 6 } \right\}$$ ;

Question 7

Solve the problem.
-Daryl borrows $3,750 at a rate of 10.5% compounded semiannually. Find how much Daryl owes at the end of 5 years. Use: $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ where:
$A =$ final amount
$P = \$ 3,750$ (the amount borrowed)
$\mathrm { r } = 10.5 \% = 0.105$ (the annual rate of interest)
$\mathrm { n } = 2$ (the number of times interest is compounded each year)
$t = 5$ (the duration of the loan in years)

Accepted Answer

A)  $\$ 4,843.30$ 
B)  $\$ 6,880.90$ 
C)  $\$ 39,468.75$ 
D)  $\$ 6,255.36$ 
A)  $\$ 4,843.30$ 
B)  $\$ 6,880.90$ 
C)  $\$ 39,468.75$ 
D)  $\$ 6,255.36$

Question 8

Solve the problem.
-The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential
Growth model A $\mathrm { A } = 1,400 \mathrm { e } ^ { 0.047 \mathrm { t } }$ . When will the account be worth $1,856?

Accepted Answer

A)  2006 
B)  2005 
C)  2007 
D)  2008 
A)  2006 
B)  2005 
C)  2007 
D)  2008

Question 9

Use a calculator to find the natural logarithm correct to four decimal places.
-$\ln 0.983$

Accepted Answer

A)  $0.0171$ 
B)  $- 0.0171$ 
C)  $- 0.0074$ 
D)  $0.0074$ 
A)  $0.0171$ 
B)  $- 0.0171$ 
C)  $- 0.0074$ 
D)  $0.0074$

Question 10

For the given functions f and g, find the requested composite function value.
-$$f ( x ) = 2 x + 2 , \quad g ( x ) = 2 x ^ { 2 } + 1 ; \quad \text { Find } ( f \circ f ) ( 0 )$$

Accepted Answer

A)  4 
B)  3 
C)  9 
D)  6 
A)  4 
B)  3 
C)  9 
D)  6

Question 11

The graph of an exponential function is given. Match the graph to one of the following functions.
-  A) $f ( x ) = 4 ^ { x }$

Accepted Answer

B)  $f ( x ) = 4 ^ { x } - 2$ 
C)  $f ( x ) = 4 ^ { x + 2 }$ 
D)  $f ( x ) = 4 ^ { x } + 2$ 
B)  $f ( x ) = 4 ^ { x } - 2$ 
C)  $f ( x ) = 4 ^ { x + 2 }$ 
D)  $f ( x ) = 4 ^ { x } + 2$

Question 12

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of
the inverse.
-$$f ( x ) = \frac { 3 } { x - 1 }$$

Accepted Answer

A)  $f ( x ) : D = \{ x \mid x \neq - 3 \} , R = \{ y | y \neq 1 \rangle$; 
$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } | \mathrm { x } \neq 1 \rangle , R = \{ \mathrm { y } \mid \mathrm { y } \neq - 3 \}$ 
B)  $f ( x )$ : D is all real numbers, $R = \{ y | y \neq - 3 \rangle$;
 $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq - 3 \} , \mathrm { R }$ is all real numbers 
C)  $f ( x ) : D = \{ x \mid x \neq 1 \} , R = \{ y \neq 0 \}$;
$$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq 0 \} , \mathrm { R } = \{ \mathrm { y } \mid \mathrm { y } \neq 1 \}$$ 
D)  $f ( x )$ : $D$ is all real numbers, $R$ is all real numbers; 
$f ^ { - 1 } ( x )$ : $D$ is all real numbers, $R$ is all real numbers 
A)  $f ( x ) : D = \{ x \mid x \neq - 3 \} , R = \{ y | y \neq 1 \rangle$; 
$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } | \mathrm { x } \neq 1 \rangle , R = \{ \mathrm { y } \mid \mathrm { y } \neq - 3 \}$ 
B)  $f ( x )$ : D is all real numbers, $R = \{ y | y \neq - 3 \rangle$;
 $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq - 3 \} , \mathrm { R }$ is all real numbers 
C)  $f ( x ) : D = \{ x \mid x \neq 1 \} , R = \{ y \neq 0 \}$;
$$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq 0 \} , \mathrm { R } = \{ \mathrm { y } \mid \mathrm { y } \neq 1 \}$$ 
D)  $f ( x )$ : $D$ is all real numbers, $R$ is all real numbers; 
$f ^ { - 1 } ( x )$ : $D$ is all real numbers, $R$ is all real numbers

Question 13

Find a formula for the inverse of the function described below.
-A size 4 dress in Country $C$ is size 42 in Country D. A function that converts dress sizes in Country $C$ to those in Country $D$ is $f ( x ) = x + 38$.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x - 38$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { - 38 }$ 
C)  $f ^ { - 1 } ( x ) = x + 38$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 38 }$ 
A)  $f ^ { - 1 } ( x ) = x - 38$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { - 38 }$ 
C)  $f ^ { - 1 } ( x ) = x + 38$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 38 }$

Question 14

For the given functions f and g, find the requested composite function value.
-$f ( x ) = \left| 20 x ^ { 2 } - 4 x \right| , \quad g ( x ) = 12 x - 4 ; \quad$ Find $( f \circ g ) ( 4 )$

Accepted Answer

A)  34,900 
B)  38,544 
C)  3,644 
D)  13,376 
A)  34,900 
B)  38,544 
C)  3,644 
D)  13,376

Question 15

Indicate whether the function is one-to-one.
-{(6, -6), (12, -5), (10, -4), (8, -3)}

Accepted Answer

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

Question 16

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

Question 17

Graph the function.
-$$\begin{array} { l } 
f ( x ) = e ^ { 3 x } - 1 \

\end{array}$$

A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 18

Solve the given exponential equation. Round answer to three decimal places.
-$2 ^ { x } - 3 x - 3 = 0$

Accepted Answer

A)  {3.868} 
B)  {14.605} 
C)  {-0.899} 
D)  {-0.899, 3.868} 
A)  {3.868} 
B)  {14.605} 
C)  {-0.899} 
D)  {-0.899, 3.868}

Question 19

Solve the problem.
-The surface area $S$ (in square inches) of a cylindrical pipe with length 12 inches is given by $S ( r ) = 2 \pi r ^ { 2 } + 24 \pi r$, where $r$ is the radius of the piston (in inches). If the radius is increasing with time $t$ (in minutes) according to the formula $r ( t ) = \frac { 1 } { 6 } t ^ { 2 } , t \geq 0$, find the surface area $S$ of the pipe as a function of the time $t$.

Accepted Answer

The answer of Solve the problem.
-The surface area $S$ (in...

Question 20

Solve the problem.
-Find the amount owed at the end of 8 years if $5000 is loaned at a rate of 5% compounded monthly.

Accepted Answer

A)  $8060.16 
B)  $12,911.25 
C)  $7452.93 
D)  $9093.60 
A)  $8060.16 
B)  $12,911.25 
C)  $7452.93 
D)  $9093.60

Find the domain of the function. - $f ( x ) = \log _ { 9 } ( x + 8 ) ^ { 2 }$

Evaluate the expression using the values given in the table. - (gf)(1) x 1 6 10 12 f(x) -2 10 3 12 -5 -2 1 3 () 1 -5 6 10

For the given functions f and g, find the requested composite function. - $f ( x ) = 4 x ^ { 2 } + 6 x + 3 , \quad g ( x ) = 6 x - 7 ; \quad$ Find $( g \circ f ) ( x )$

Solve the problem. -The half-life of silicon-32 is 710 years. If 10 grams is present now, how much will be present in 800 years? (Round your answer to three decimal places.)

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. - $f ( x ) = \frac { 4 } { 6 x + 5 }$

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln 0.983$

For the given functions f and g, find the requested composite function value. - $f ( x ) = 2 x + 2 , \quad g ( x ) = 2 x ^ { 2 } + 1 ; \quad \text { Find } ( f \circ f ) ( 0 )$

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. - $f ( x ) = \frac { 3 } { x - 1 }$

Find a formula for the inverse of the function described below. -A size 4 dress in Country $C$ is size 42 in Country D. A function that converts dress sizes in Country $C$ to those in Country $D$ is $f ( x ) = x + 38$ .

For the given functions f and g, find the requested composite function value. - $f ( x ) = \left| 20 x ^ { 2 } - 4 x \right| , \quad g ( x ) = 12 x - 4 ; \quad$ Find $( f \circ g ) ( 4 )$

Indicate whether the function is one-to-one. -{(6, -6), (12, -5), (10, -4), (8, -3)}

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

Solve the given exponential equation. Round answer to three decimal places. - $2 ^ { x } - 3 x - 3 = 0$

Solve the problem. -Find the amount owed at the end of 8 years if $5000 is loaned at a rate of 5% compounded monthly.

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

Review

Filters

Exam 4: Exponential and Logarithmic Functions

Find the domain of the function. - f(x)=log⁡9(x+8)2f ( x ) = \log _ { 9 } ( x + 8 ) ^ { 2 }f(x)=log9​(x+8)2