Question 1

Give the domain and range of the relation.
-

Accepted Answer

A)  domain: $\{ 4,8,12 \}$; range: $\{ 5,7,13 \}$ 
B)  None of these 
C)  domain: $\{ 4,7,12 \}$; range: $\{ 5,8,13 \}$ 
D)  domain: $\{ 5,8,13 \}$; range: $\{ 4,7,12 \}$ 
A)  domain: $\{ 4,8,12 \}$; range: $\{ 5,7,13 \}$ 
B)  None of these 
C)  domain: $\{ 4,7,12 \}$; range: $\{ 5,8,13 \}$ 
D)  domain: $\{ 5,8,13 \}$; range: $\{ 4,7,12 \}$

Question 2

Give the domain and range of the relation.
-

Accepted Answer

A)  domain: $( 5 , \infty )$; range: $( 2 , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $[ 5 , \infty )$ 
D)  domain: $[ 5 , \infty )$; range: $( - \infty , \infty )$ 
A)  domain: $( 5 , \infty )$; range: $( 2 , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $[ 5 , \infty )$ 
D)  domain: $[ 5 , \infty )$; range: $( - \infty , \infty )$

Question 3

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope -intercept form.
-

Accepted Answer

A)  $y = - 5$ 
B)  $x = - 5$ 
C)  $y = 5$ 
D)  $x = 5$ 
A)  $y = - 5$ 
B)  $x = - 5$ 
C)  $y = 5$ 
D)  $x = 5$

Question 4

Compute and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$
-$$f ( x ) = 9 x - 11$$

Accepted Answer

A)  $\frac { 11 } { 9 }$ 
B)  -11h 
C)  9 
D)  11 
A)  $\frac { 11 } { 9 }$ 
B)  -11h 
C)  9 
D)  11

Question 5

The figure below shows the graph of a function y = f(x). Use this graph to solve the problem.
-$$\text { Sketch the graph of } y = 2 f ( x ) \text {. }$$

Accepted Answer

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

Question 6

The figure below shows the graph of a function y = f(x). Use this graph to solve the problem.
-$$\text { Sketch the graph of } y = - f ( x ) \text {. }$$

Accepted Answer

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

Question 7

Decide whether the relation defines a function.
-Student Test Score

Accepted Answer

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

Question 8

Describe how the graph of the equation relates to the graph of y = x2.
-$$f ( x ) = \frac { 1 } { 4 } x ^ { 2 } - 5$$

Accepted Answer

A)  vertical stretching by a factor of 4 and a translation 5 units down 
B)  vertical shrinking by a factor of $\frac { 1 } { 4 }$ and a translation 5 units to the left 
C)  vertical stretching by a factor of 4 and a translation 5 units to the right 
D)  vertical shrinking by a factor of $\frac { 1 } { 4 }$ and a translation 5 units down 
A)  vertical stretching by a factor of 4 and a translation 5 units down 
B)  vertical shrinking by a factor of $\frac { 1 } { 4 }$ and a translation 5 units to the left 
C)  vertical stretching by a factor of 4 and a translation 5 units to the right 
D)  vertical shrinking by a factor of $\frac { 1 } { 4 }$ and a translation 5 units down

Question 9

Find the slope of the line and sketch the graph.
-$-4 y=3 x$

Accepted Answer

A)  $m = - \frac { 4 } { 3 }$
  
B)  $\mathrm { m } = - \frac { 3 } { 4 }$
  
C)  $\mathrm { m } = \frac { 4 } { 3 }$
  
D)  $\mathrm { m } = \frac { 3 } { 4 }$
  
A)  $m = - \frac { 4 } { 3 }$
  
B)  $\mathrm { m } = - \frac { 3 } { 4 }$
  
C)  $\mathrm { m } = \frac { 4 } { 3 }$
  
D)  $\mathrm { m } = \frac { 3 } { 4 }$

Question 10

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$\mathrm { P } ( 5 \sqrt { 3 } , - \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 3 } , 0 )$

Accepted Answer

A)  $\left( 2 \sqrt { 3 } , - \frac { \sqrt { 10 } } { 2 } \right)$ 
B)  $( - 3,10 )$ 
C)  $\left( 2 \sqrt { 6 } , - \frac { \sqrt { 30 } } { 2 } \right)$ 
D)  $\left( 3 \sqrt { 3 } , \frac { \sqrt { 10 } } { 2 } \right)$ 
A)  $\left( 2 \sqrt { 3 } , - \frac { \sqrt { 10 } } { 2 } \right)$ 
B)  $( - 3,10 )$ 
C)  $\left( 2 \sqrt { 6 } , - \frac { \sqrt { 30 } } { 2 } \right)$ 
D)  $\left( 3 \sqrt { 3 } , \frac { \sqrt { 10 } } { 2 } \right)$

Question 11

Determine whether the three points are the vertices of a right triangle.
-$$( - 5 , - 8 ) , ( 0 , - 8 ) , ( 0 , - 2 )$$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 12

Use a graphing calculator to solve the linear equation.
-The graph of $y _ { 1 }$ is shown in the standard viewing window. Which is the only choice that could possibly be the solution of the equation $y _ { 1 } = 0$ ?

$- 12 , - \frac { 13 } { 4 } , 3,12$

Accepted Answer

A)  12 
B)  3 
C)  $- 12$ 
D)  $- \frac { 13 } { 4 }$ 
A)  12 
B)  3 
C)  $- 12$ 
D)  $- \frac { 13 } { 4 }$

Question 13

Find the center-radius form of the equation of the circle.
-center $( 0,2 )$, radius $\sqrt { 19 }$

Accepted Answer

A)  $x ^ { 2 } + ( y + 2 ) ^ { 2 } = 19$ 
B)  $( x - 2 ) ^ { 2 } + y ^ { 2 } = 361$ 
C)  $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 19$ 
D)  $( x + 2 ) ^ { 2 } + y ^ { 2 } = 361$ 
A)  $x ^ { 2 } + ( y + 2 ) ^ { 2 } = 19$ 
B)  $( x - 2 ) ^ { 2 } + y ^ { 2 } = 361$ 
C)  $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 19$ 
D)  $( x + 2 ) ^ { 2 } + y ^ { 2 } = 361$

Question 14

Refer to the following graphs to determine an appropriate response.  
-Which one is the graph of $y = x ^ { 3 }$ ? What is its range?

Accepted Answer

A)  graph $C ; [ - 2,2 ]$ 
B)  graph A; $( - \infty , \infty )$ 
C)  graph B; $( - \infty , \infty )$ 
D)  graph $D ; [ 0 , \infty )$ 
A)  graph $C ; [ - 2,2 ]$ 
B)  graph A; $( - \infty , \infty )$ 
C)  graph B; $( - \infty , \infty )$ 
D)  graph $D ; [ 0 , \infty )$

Question 15

Graph the function.
-$f(x)=x^{3}+5$

Accepted Answer

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

Question 16

Give the domain and range of the relation.
-Annual New Telemarketing Companies

Accepted Answer

A)  domain: $\{ 52,102,170,187,218 \}$; range: $\{ 1993,1994,1995,1996,1997 \}$ 
B)  None of these 
C)  domain: $\{ 1993,1994,1995,1996,1997 \}$; range: $\{ 52,102,170,187,218 \}$ 
D)  domain: $\{$ Year $\}$; range: $\{$ Number $\}$ 
A)  domain: $\{ 52,102,170,187,218 \}$; range: $\{ 1993,1994,1995,1996,1997 \}$ 
B)  None of these 
C)  domain: $\{ 1993,1994,1995,1996,1997 \}$; range: $\{ 52,102,170,187,218 \}$ 
D)  domain: $\{$ Year $\}$; range: $\{$ Number $\}$

Question 17

Determine the intervals of the domain for which the function is increasing, decreasing, and constant.
-

Accepted Answer

A) $\text { Increasing }(-\infty, 0] \text {; Decreasing }[0,-\infty)$ 
B)  Increasing $( - \infty , 0 ]$; Decreasing $( - \infty , 0 ]$ 
C)  Increasing $[ 0 , \infty )$; Decreasing $( - \infty , 0 ]$ 
D)  Increasing $( - \infty , 0 ]$; Decreasing $[ 0 , \infty )$ 
A) $\text { Increasing }(-\infty, 0] \text {; Decreasing }[0,-\infty)$ 
B)  Increasing $( - \infty , 0 ]$; Decreasing $( - \infty , 0 ]$ 
C)  Increasing $[ 0 , \infty )$; Decreasing $( - \infty , 0 ]$ 
D)  Increasing $( - \infty , 0 ]$; Decreasing $[ 0 , \infty )$

Question 18

Solve the problem.
-Select the equation that describes the graph shown.

Accepted Answer

A)  $y = ( x - 3 ) ^ { 2 } + 2$ 
B)  $y = ( x + 3 ) ^ { 2 }$ 
C)  $y = ( x - 3 ) ^ { 2 }$ 
D)  $\mathrm { y } = \mathrm { x } ^ { 2 } - 3$ 
A)  $y = ( x - 3 ) ^ { 2 } + 2$ 
B)  $y = ( x + 3 ) ^ { 2 }$ 
C)  $y = ( x - 3 ) ^ { 2 }$ 
D)  $\mathrm { y } = \mathrm { x } ^ { 2 } - 3$

Question 19

Give the domain and range of the relation.
-$$y = ( x - 5 ) ^ { 2 } + 5$$

Accepted Answer

A)  domain: $( - \infty , 5 )$; range: $( - \infty , \infty )$ 
B)  domain: $( - 5 , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , 5 )$ 
D)  domain: $( - \infty , \infty )$; range: $[ 5 , \infty )$ 
A)  domain: $( - \infty , 5 )$; range: $( - \infty , \infty )$ 
B)  domain: $( - 5 , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , 5 )$ 
D)  domain: $( - \infty , \infty )$; range: $[ 5 , \infty )$

Question 20

Solve the problem.
-Suppose a car rental company charges $146 for the first day and $96 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(6.5).

Accepted Answer

A)  $624 
B)  $722 
C)  $770 
D)  $674 
A)  $624 
B)  $722 
C)  $770 
D)  $674

Give the domain and range of the relation. -

Give the domain and range of the relation. -

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope -intercept form. -

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = 9 x - 11$

Decide whether the relation defines a function. -Student Test Score

Describe how the graph of the equation relates to the graph of y = x2. - $f ( x ) = \frac { 1 } { 4 } x ^ { 2 } - 5$

Find the slope of the line and sketch the graph. - $-4 y=3 x$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 5 \sqrt { 3 } , - \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 3 } , 0 )$

Determine whether the three points are the vertices of a right triangle. - $( - 5 , - 8 ) , ( 0 , - 8 ) , ( 0 , - 2 )$

Find the center-radius form of the equation of the circle. -center $( 0,2 )$ , radius $\sqrt { 19 }$

Refer to the following graphs to determine an appropriate response. $Refer to the following graphs to determine an appropriate response. -Which one is the graph of y = x ^ { 3 } ? What is its range?$ -Which one is the graph of $y = x ^ { 3 }$ ? What is its range?

Graph the function. - $f(x)=x^{3}+5$ $Graph the function. - f(x)=x^{3}+5$

Give the domain and range of the relation. -Annual New Telemarketing Companies

Determine the intervals of the domain for which the function is increasing, decreasing, and constant. -

Solve the problem. -Select the equation that describes the graph shown.

Give the domain and range of the relation. - $y = ( x - 5 ) ^ { 2 } + 5$

Solve the problem. -Suppose a car rental company charges $146 for the first day and $96 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(6.5).

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic 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

Review of Basic Concepts

Filters

Exam 2: Graphs and Functions

Give the domain and range of the relation. -

Give the domain and range of the relation. -

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope -intercept form. -

Compute and simplify the difference quotient f(x+h)−f(x)h,h≠0\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0hf(x+h)−f(x)​,h=0 - f(x)=9x−11f ( x ) = 9 x - 11f(x)=9x−11

The figure below shows the graph of a function y = f(x). Use this graph to solve the problem. - Sketch the graph of y=2f(x). \text { Sketch the graph of } y = 2 f ( x ) \text {. } Sketch the graph of y=2f(x).

The figure below shows the graph of a function y = f(x). Use this graph to solve the problem. - Sketch the graph of y=−f(x). \text { Sketch the graph of } y = - f ( x ) \text {. } Sketch the graph of y=−f(x).

Decide whether the relation defines a function. -Student Test Score

Describe how the graph of the equation relates to the graph of y = x2. - f(x)=14x2−5f ( x ) = \frac { 1 } { 4 } x ^ { 2 } - 5f(x)=41​x2−5

Find the slope of the line and sketch the graph. - −4y=3x-4 y=3 x−4y=3x

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(53,−10),Q(−3,0)\mathrm { P } ( 5 \sqrt { 3 } , - \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 3 } , 0 )P(53​,−10​),Q(−3​,0)

Determine whether the three points are the vertices of a right triangle. - (−5,−8),(0,−8),(0,−2)( - 5 , - 8 ) , ( 0 , - 8 ) , ( 0 , - 2 )(−5,−8),(0,−8),(0,−2)

Find the center-radius form of the equation of the circle. -center (0,2)( 0,2 )(0,2) , radius 19\sqrt { 19 }19​

Refer to the following graphs to determine an appropriate response. -Which one is the graph of y=x3y = x ^ { 3 }y=x3 ? What is its range?

Graph the function. - f(x)=x3+5f(x)=x^{3}+5f(x)=x3+5

Give the domain and range of the relation. -Annual New Telemarketing Companies

Determine the intervals of the domain for which the function is increasing, decreasing, and constant. -

Solve the problem. -Select the equation that describes the graph shown.

Give the domain and range of the relation. - y=(x−5)2+5y = ( x - 5 ) ^ { 2 } + 5y=(x−5)2+5

Solve the problem. -Suppose a car rental company charges $146 for the first day and $96 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(6.5).

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic 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

Review of Basic Concepts

Filters

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = 9 x - 11$

Describe how the graph of the equation relates to the graph of y = x2. - $f ( x ) = \frac { 1 } { 4 } x ^ { 2 } - 5$

Find the slope of the line and sketch the graph. - $-4 y=3 x$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 5 \sqrt { 3 } , - \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 3 } , 0 )$

Determine whether the three points are the vertices of a right triangle. - $( - 5 , - 8 ) , ( 0 , - 8 ) , ( 0 , - 2 )$

Find the center-radius form of the equation of the circle. -center $( 0,2 )$ , radius $\sqrt { 19 }$

Refer to the following graphs to determine an appropriate response. $Refer to the following graphs to determine an appropriate response. -Which one is the graph of y = x ^ { 3 } ? What is its range?$ -Which one is the graph of $y = x ^ { 3 }$ ? What is its range?

Graph the function. - $f(x)=x^{3}+5$ $Graph the function. - f(x)=x^{3}+5$

Give the domain and range of the relation. - $y = ( x - 5 ) ^ { 2 } + 5$