Question 1

Evaluate as indicated.
-Find $f ( a + 2 )$ for the given function.
$$f ( x ) = \sqrt { x - 5 }$$

Accepted Answer

A)  $\sqrt { x + a - 3 }$ 
B)  $\sqrt { a - 3 }$ 
C)  $\sqrt { a - 10 }$ 
D)  $\sqrt { x + a - 10 }$ 
A)  $\sqrt { x + a - 3 }$ 
B)  $\sqrt { a - 3 }$ 
C)  $\sqrt { a - 10 }$ 
D)  $\sqrt { x + a - 10 }$

Question 2

Use transformations to graph the given function.
-$$p ( x ) = - 3 | x + 3 | - 1$$

Accepted Answer

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

Question 3

Solve the problem.
-A car accelerates from 0 to $91.2 \mathrm { ft } / \mathrm { sec }$ in $8 \mathrm { sec }$. The distance $d ( t )$ (in $\mathrm { ft }$ ) that the car travels $t$ seconds after motion begins is given by $d ( t ) = 5.7 t ^ { 2 }$, where $0 \leq t \leq 8$.
a. Find the difference quotient $\frac { d ( t + h ) - d ( t ) } { h }$.
b. Use the difference quotient to determine the average rate of speed on the interval $4 \leq \mathrm { t } \leq 6$.

Accepted Answer

A)  a. $5.7 ( t + h )$;
b. $34.2 \mathrm { ft } / \mathrm { sec }$ 
B)  a. $11.4 t + 5.7 h$;
b. $57 \mathrm { ft } / \mathrm { sec }$ 
C)  a. $5.7 ( t + h )$;
b. $79.8 \mathrm { ft } / \mathrm { sec }$ 
D)  a. $11.4 t + 5.7 h$;
b. $79.8 \mathrm { ft } / \mathrm { sec }$ 
A)  a. $5.7 ( t + h )$;
b. $34.2 \mathrm { ft } / \mathrm { sec }$ 
B)  a. $11.4 t + 5.7 h$;
b. $57 \mathrm { ft } / \mathrm { sec }$ 
C)  a. $5.7 ( t + h )$;
b. $79.8 \mathrm { ft } / \mathrm { sec }$ 
D)  a. $11.4 t + 5.7 h$;
b. $79.8 \mathrm { ft } / \mathrm { sec }$

Question 4

Find the slope of the secant line indicated with a dashed line.
-

Accepted Answer

A)  $m = \frac { 4 } { 9 }$ 
B)  $m = - \frac { 4 } { 9 }$ 
C)  $m = \frac { 9 } { 4 }$ 
D)  $m = - \frac { 9 } { 4 }$ 
A)  $m = \frac { 4 } { 9 }$ 
B)  $m = - \frac { 4 } { 9 }$ 
C)  $m = \frac { 9 } { 4 }$ 
D)  $m = - \frac { 9 } { 4 }$

Question 5

Use the graph of y = f (x) to answer the questions.
-a. Determine the domain 
b. Determine the $x$-intercept
$\text { b. Determine the } x \text {-intercept }$

Accepted Answer

A)  Domain: $( - \infty , \infty ) ; x$-intercept $( 0 , - 1 )$ 
B)  Domain: $[ - 5,0 ] \cup \{ 2 \} ; x$-intercept $( - 1,0 )$ 
C)  Domain: $( - \infty , 4 ) ; x$-intercept $( - 1,0 )$ 
D)  Domain: $[ - 5,0 ] ; x$-intercept $( 0 , - 1 )$ 
A)  Domain: $( - \infty , \infty ) ; x$-intercept $( 0 , - 1 )$ 
B)  Domain: $[ - 5,0 ] \cup \{ 2 \} ; x$-intercept $( - 1,0 )$ 
C)  Domain: $( - \infty , 4 ) ; x$-intercept $( - 1,0 )$ 
D)  Domain: $[ - 5,0 ] ; x$-intercept $( 0 , - 1 )$

Question 6

Produce a rule for the function whose graph is shown.
-A math tutor makes $15.00 per hour in the tutoring lab at her school. During final exam week, she earns overtime at $22.50 per hour for the work exceeding her normal 40-hr work week. Which
Graph best depicts her total salary for the week as a function of the number of hours worked?

Accepted Answer

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

Question 7

Identify the domain and range of the relation, and determine whether the relation is a function.
-$$\{ ( - 7 , - 12 ) , ( - 3 , - 5 ) , ( 1,16 ) , ( 8,18 ) \}$$

Accepted Answer

A)  Domain: $\{ - 12 , - 5,16,18 \}$; Range: $\{ - 7 , - 3,1,8 \}$; Function 
B)  Domain: $\{ - 7 , - 3,1,8 \}$; Range: $\{ - 12 , - 5,16,18 \}$; Not a function 
C)  Domain: $\{ - 7 , - 3,1,8 \}$; Range: $\{ - 12 , - 5,16,18 \}$; Function 
D)  Domain: $\{ - 12 , - 5,16,18 \}$; Range: $\{ - 7 , - 3,1,8 \}$; Not a function 
A)  Domain: $\{ - 12 , - 5,16,18 \}$; Range: $\{ - 7 , - 3,1,8 \}$; Function 
B)  Domain: $\{ - 7 , - 3,1,8 \}$; Range: $\{ - 12 , - 5,16,18 \}$; Not a function 
C)  Domain: $\{ - 7 , - 3,1,8 \}$; Range: $\{ - 12 , - 5,16,18 \}$; Function 
D)  Domain: $\{ - 12 , - 5,16,18 \}$; Range: $\{ - 7 , - 3,1,8 \}$; Not a function

Question 8

Use transformations to graph the given function.
-$$f ( x ) = \frac { 1 } { 2 } | x + 2 | + 3$$

Accepted Answer

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

Question 9

Determine whether the relation defines y as a function of x.
-

Accepted Answer

A)  Not a function 
B)  Function 
A)  Not a function 
B)  Function

Question 10

Determine the domain and range of the function.
-

Accepted Answer

A)  Domain: $( - \infty , \infty )$; Range $( - \infty , 1 ]$ 
B)  Domain: $( - \infty , 1 ]$; Range $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range $( - \infty , \infty )$ 
D)  Domain: $( - \infty , 1 ]$; Range $[ 3 , \infty )$ 
A)  Domain: $( - \infty , \infty )$; Range $( - \infty , 1 ]$ 
B)  Domain: $( - \infty , 1 ]$; Range $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range $( - \infty , \infty )$ 
D)  Domain: $( - \infty , 1 ]$; Range $[ 3 , \infty )$

Question 11

Use the given information to
a. Graph the function.
b. Write the domain in interval notation.
c. Write the range in interval notation.
-$f ( x ) = \left\{ \begin{array} { l l } - x ^ { 2 } - 2 & \text { for } x \leq 1 \ \frac { 1 } { 2 } x & \text { for } x > 1 \end{array} \right.$

Accepted Answer

A)  domain: $( - \infty , \infty )$
range: $( - \infty , - 2 ) \cup \left( \frac { 1 } { 2 } , \infty \right)$
  
B)  domain: $( - \infty , \infty )$
range: $( - \infty , - 2 ) \cup \left( \frac { 1 } { 2 } , \infty \right)$
  
C)  domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$
  
D)  domain: $( - \infty , \infty )$
range: $\left( - \infty , \frac { 1 } { 2 } \right)$
  
A)  domain: $( - \infty , \infty )$
range: $( - \infty , - 2 ) \cup \left( \frac { 1 } { 2 } , \infty \right)$
  
B)  domain: $( - \infty , \infty )$
range: $( - \infty , - 2 ) \cup \left( \frac { 1 } { 2 } , \infty \right)$
  
C)  domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$
  
D)  domain: $( - \infty , \infty )$
range: $\left( - \infty , \frac { 1 } { 2 } \right)$

Question 12

Write a piecewise-defined function to model the monthly cost C(x) (in $) as a function of the number of minutes used x for the month.
-A cell phone plan charges $\$ 45.75$ per month, plus $\$ 9.55$ in taxes, plus $\$ 0.35$ per minute for calls beyond the 500 -min monthly limit.

Accepted Answer

A)  $C ( x ) = \left\{ \begin{array} { l l } 55.3 , & \text { for } x \leq 500 \ 55.3 + 0.35 ( x - 500 ) , & \text { for } x > 500 \end{array} \right.$ 
B)  $C ( x ) = \left\{ \begin{array} { l l } 55.3 , & \text { for } x \leq 500 \ 0.35 x , & \text { for } x > 500 \end{array} \right.$ 
C)  $C ( x ) = \left\{ \begin{array} { l l } 55.3 , & \text { for } x \leq 500 \ 55.3 + 0.35 x , & \text { for } x > 500 \end{array} \right.$ 
D)  $C ( x ) = \left\{ \begin{array} { l l } 55.3 , & \text { for } x \leq 500 \ 0.35 ( x - 500 ) , & \text { for } x > 500 \end{array} \right.$ 
A)  $C ( x ) = \left\{ \begin{array} { l l } 55.3 , & \text { for } x \leq 500 \ 55.3 + 0.35 ( x - 500 ) , & \text { for } x > 500 \end{array} \right.$ 
B)  $C ( x ) = \left\{ \begin{array} { l l } 55.3 , & \text { for } x \leq 500 \ 0.35 x , & \text { for } x > 500 \end{array} \right.$ 
C)  $C ( x ) = \left\{ \begin{array} { l l } 55.3 , & \text { for } x \leq 500 \ 55.3 + 0.35 x , & \text { for } x > 500 \end{array} \right.$ 
D)  $C ( x ) = \left\{ \begin{array} { l l } 55.3 , & \text { for } x \leq 500 \ 0.35 ( x - 500 ) , & \text { for } x > 500 \end{array} \right.$

Question 13

Determine the slope of the line.
-

Accepted Answer

A)  $m = - \frac { 5 } { 3 }$ 
B)  $m = \frac { 3 } { 5 }$ 
C)  $m = - \frac { 3 } { 5 }$ 
D)  $m = \frac { 5 } { 3 }$ 
A)  $m = - \frac { 5 } { 3 }$ 
B)  $m = \frac { 3 } { 5 }$ 
C)  $m = - \frac { 3 } { 5 }$ 
D)  $m = \frac { 5 } { 3 }$

Question 14

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form.
-The line passes through $( 12,9 )$ and $( 9,9 )$.

Accepted Answer

A)  $y = - \frac { 1 } { 6 } x + \frac { 21 } { 2 }$ 
B)  $y = - \frac { 1 } { 6 } x - \frac { 21 } { 2 }$ 
C)  $x = 9$ 
D)  $y = 9$ 
A)  $y = - \frac { 1 } { 6 } x + \frac { 21 } { 2 }$ 
B)  $y = - \frac { 1 } { 6 } x - \frac { 21 } { 2 }$ 
C)  $x = 9$ 
D)  $y = 9$

Question 15

Determine whether the relation defines y as a function of x.
-$x = | y + 1 |$

Accepted Answer

A)  Function 
B)  Not a function 
A)  Function 
B)  Not a function

Question 16

Find two functions f and g such that $h ( x ) = ( f \circ g ) ( x )$
-$$h ( x ) = \sqrt [ 5 ] { 8 x - 3 }$$

Accepted Answer

A)  $f ( x ) = 8 x - 3$ and $g ( x ) = \sqrt [ 5 ] { x }$ 
B)  $f ( x ) = x - 3$ and $g ( x ) = \sqrt [ 5 ] { 8 x }$ 
C)  $f ( x ) = \sqrt [ 5 ] { x }$ and $g ( x ) = 8 x - 3$ 
D)  $f ( x ) = \sqrt [ 5 ] { 8 x }$ and $g ( x ) = x - 3$ 
A)  $f ( x ) = 8 x - 3$ and $g ( x ) = \sqrt [ 5 ] { x }$ 
B)  $f ( x ) = x - 3$ and $g ( x ) = \sqrt [ 5 ] { 8 x }$ 
C)  $f ( x ) = \sqrt [ 5 ] { x }$ and $g ( x ) = 8 x - 3$ 
D)  $f ( x ) = \sqrt [ 5 ] { 8 x }$ and $g ( x ) = x - 3$

Question 17

Use the slope-intercept form to write an equation of the line that passes through the given point and has
the given slope. Use function notation where y = f(x).
-$$( - 3,1 ) ; m = - \frac { 2 } { 3 }$$

Accepted Answer

A)  $f ( x ) = - \frac { 2 } { 3 } x + 5$ 
B)  $f ( x ) = \frac { 2 } { 3 } x - 1$ 
C)  $f ( x ) = - \frac { 2 } { 3 } x - 3$ 
D)  $f ( x ) = - \frac { 2 } { 3 } x - 1$ 
A)  $f ( x ) = - \frac { 2 } { 3 } x + 5$ 
B)  $f ( x ) = \frac { 2 } { 3 } x - 1$ 
C)  $f ( x ) = - \frac { 2 } { 3 } x - 3$ 
D)  $f ( x ) = - \frac { 2 } { 3 } x - 1$

Question 18

Write the domain in interval notation.
-$$k ( x ) = \frac { x + 9 } { x - 4 }$$

Accepted Answer

A)  $( - \infty , 9 ) \cup ( 9 , \infty )$ 
B)  $( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
C)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
D)  $( - \infty , - 9 ) \cup ( - 9 , \infty )$ 
A)  $( - \infty , 9 ) \cup ( 9 , \infty )$ 
B)  $( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
C)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
D)  $( - \infty , - 9 ) \cup ( - 9 , \infty )$

Question 19

Evaluate the function for the given value of x.
-$$f ( x ) = - 2 x , g ( x ) = \frac { 1 } { x + 2 } , ( f - g ) ( 1 ) = ?$$

Accepted Answer

A)  $( f - g ) ( 1 ) = - \frac { 5 } { 3 }$ 
B)  $( f - g ) ( 1 ) = \frac { 5 } { 3 }$ 
C)  $( f - g ) ( 1 ) = - \frac { 7 } { 3 }$ 
D)  $( f - g ) ( 1 ) = \frac { 7 } { 3 }$ 
A)  $( f - g ) ( 1 ) = - \frac { 5 } { 3 }$ 
B)  $( f - g ) ( 1 ) = \frac { 5 } { 3 }$ 
C)  $( f - g ) ( 1 ) = - \frac { 7 } { 3 }$ 
D)  $( f - g ) ( 1 ) = \frac { 7 } { 3 }$

Question 20

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-$$\text { The graph of } y = \frac { 1 } { 3 } f ( x ) \text { is the graph of } y = f ( x ) \text { with a (choose one: vertical stretch, vertical shrink, }$$ horizontal stretch, horizontal shrink).

Accepted Answer

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

Evaluate as indicated. -Find $f ( a + 2 )$ for the given function. $f ( x ) = \sqrt { x - 5 }$

Use transformations to graph the given function. - $p ( x ) = - 3 | x + 3 | - 1$

Find the slope of the secant line indicated with a dashed line. -

Identify the domain and range of the relation, and determine whether the relation is a function. - $\{ ( - 7 , - 12 ) , ( - 3 , - 5 ) , ( 1,16 ) , ( 8,18 ) \}$

Use transformations to graph the given function. - $f ( x ) = \frac { 1 } { 2 } | x + 2 | + 3$

Determine whether the relation defines y as a function of x. -

Determine the domain and range of the function. -

Use the given information to a. Graph the function. b. Write the domain in interval notation. c. Write the range in interval notation. - $f ( x ) = \left\{ \begin{array} { l l } - x ^ { 2 } - 2 & \text { for } x \leq 1 \\ \frac { 1 } { 2 } x & \text { for } x > 1 \end{array} \right.$

Write a piecewise-defined function to model the monthly cost C(x) (in $) as a function of the number of minutes used x for the month. -A cell phone plan charges $\$ 45.75$ per month, plus $\$ 9.55$ in taxes, plus $\$ 0.35$ per minute for calls beyond the 500 -min monthly limit.

Determine the slope of the line. -

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. -The line passes through $( 12,9 )$ and $( 9,9 )$ .

Determine whether the relation defines y as a function of x. - $x = | y + 1 |$

Find two functions f and g such that $h ( x ) = ( f \circ g ) ( x )$ - $h ( x ) = \sqrt [ 5 ] { 8 x - 3 }$

Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x). - $( - 3,1 ) ; m = - \frac { 2 } { 3 }$

Write the domain in interval notation. - $k ( x ) = \frac { x + 9 } { x - 4 }$

Evaluate the function for the given value of x. - $f ( x ) = - 2 x , g ( x ) = \frac { 1 } { x + 2 } , ( f - g ) ( 1 ) = ?$

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 2: Functions and Relations

Evaluate as indicated. -Find f(a+2)f ( a + 2 )f(a+2) for the given function. f(x)=x−5f ( x ) = \sqrt { x - 5 }f(x)=x−5​

Use transformations to graph the given function. - p(x)=−3∣x+3∣−1p ( x ) = - 3 | x + 3 | - 1p(x)=−3∣x+3∣−1

Find the slope of the secant line indicated with a dashed line. -

Use the graph of y = f (x) to answer the questions. -a. Determine the domain b. Determine the xxx -intercept b. Determine the x-intercept \text { b. Determine the } x \text {-intercept } b. Determine the x-intercept

Identify the domain and range of the relation, and determine whether the relation is a function. - {(−7,−12),(−3,−5),(1,16),(8,18)}\{ ( - 7 , - 12 ) , ( - 3 , - 5 ) , ( 1,16 ) , ( 8,18 ) \}{(−7,−12),(−3,−5),(1,16),(8,18)}

Use transformations to graph the given function. - f(x)=12∣x+2∣+3f ( x ) = \frac { 1 } { 2 } | x + 2 | + 3f(x)=21​∣x+2∣+3

Determine whether the relation defines y as a function of x. -

Determine the domain and range of the function. -

Determine the slope of the line. -

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. -The line passes through (12,9)( 12,9 )(12,9) and (9,9)( 9,9 )(9,9) .

Determine whether the relation defines y as a function of x. - x=∣y+1∣x = | y + 1 |x=∣y+1∣

Find two functions f and g such that h(x)=(f∘g)(x)h ( x ) = ( f \circ g ) ( x )h(x)=(f∘g)(x) - h(x)=8x−35h ( x ) = \sqrt [ 5 ] { 8 x - 3 }h(x)=58x−3​

Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x). - (−3,1);m=−23( - 3,1 ) ; m = - \frac { 2 } { 3 }(−3,1);m=−32​

Write the domain in interval notation. - k(x)=x+9x−4k ( x ) = \frac { x + 9 } { x - 4 }k(x)=x−4x+9​

Evaluate the function for the given value of x. - f(x)=−2x,g(x)=1x+2,(f−g)(1)=?f ( x ) = - 2 x , g ( x ) = \frac { 1 } { x + 2 } , ( f - g ) ( 1 ) = ?f(x)=−2x,g(x)=x+21​,(f−g)(1)=?

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Evaluate as indicated. -Find $f ( a + 2 )$ for the given function. $f ( x ) = \sqrt { x - 5 }$

Use transformations to graph the given function. - $p ( x ) = - 3 | x + 3 | - 1$

Identify the domain and range of the relation, and determine whether the relation is a function. - $\{ ( - 7 , - 12 ) , ( - 3 , - 5 ) , ( 1,16 ) , ( 8,18 ) \}$

Use transformations to graph the given function. - $f ( x ) = \frac { 1 } { 2 } | x + 2 | + 3$

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. -The line passes through $( 12,9 )$ and $( 9,9 )$ .

Determine whether the relation defines y as a function of x. - $x = | y + 1 |$

Find two functions f and g such that $h ( x ) = ( f \circ g ) ( x )$ - $h ( x ) = \sqrt [ 5 ] { 8 x - 3 }$

Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x). - $( - 3,1 ) ; m = - \frac { 2 } { 3 }$

Write the domain in interval notation. - $k ( x ) = \frac { x + 9 } { x - 4 }$

Evaluate the function for the given value of x. - $f ( x ) = - 2 x , g ( x ) = \frac { 1 } { x + 2 } , ( f - g ) ( 1 ) = ?$