Question 1

Give the domain and range of the relation.
-

Accepted Answer

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

Question 2

Graph the line described.
-$$\text { through } ( 0,6 ) ; \mathrm { m } = - \frac { 1 } { 6 }$$

Accepted Answer

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

Question 3

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant.
-

Accepted Answer

A)  Increasing $( 0 , \infty )$; Decreasing $( - \infty , 0 )$ 
B)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , \infty )$ 
C)  Increasing $( - \infty , 0 )$; Decreasing $( - \infty , 0 )$ 
D)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , - \infty )$ 
A)  Increasing $( 0 , \infty )$; Decreasing $( - \infty , 0 )$ 
B)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , \infty )$ 
C)  Increasing $( - \infty , 0 )$; Decreasing $( - \infty , 0 )$ 
D)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , - \infty )$

Question 4

Give the domain and range of the relation.
-$$y = \frac { 14 } { 4 - x }$$

Accepted Answer

A)  domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; range: $( - \infty , \infty )$ 
A)  domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; range: $( - \infty , \infty )$

Question 5

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 6

Find the center-radius form of the circle described or graphed.
-a circle having a diameter with endpoints $( - 3,4 )$ and $( - 3 , - 4 )$

Accepted Answer

A)  $( x + 3 ) ^ { 2 } + y ^ { 2 } = 4$ 
B)  $( x + 3 ) ^ { 2 } + y ^ { 2 } = 16$ 
C)  $( x - 4 ) ^ { 2 } + y ^ { 2 } = 9$ 
D)  $x ^ { 2 } + ( y - 4 ) ^ { 2 } = 9$ 
A)  $( x + 3 ) ^ { 2 } + y ^ { 2 } = 4$ 
B)  $( x + 3 ) ^ { 2 } + y ^ { 2 } = 16$ 
C)  $( x - 4 ) ^ { 2 } + y ^ { 2 } = 9$ 
D)  $x ^ { 2 } + ( y - 4 ) ^ { 2 } = 9$

Question 7

Graph the circle.
-$$( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$$

Accepted Answer

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

Question 8

The graph of y = f(x) is given. Use the graph to find the function value.
-Find f(-12).

Accepted Answer

A)  0 
B)  20 
C)  -8 
D)  -12 
A)  0 
B)  20 
C)  -8 
D)  -12

Question 9

Graph the line described.
-through (1, 9); undefined slope

Accepted Answer

A) 
  
B) 
 
 80 
C) 
  
D) 
  
A) 
  
B) 
 
 80 
C) 
  
D)

Question 10

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 11

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$
-Select the equation that describes the graph shown.

Accepted Answer

A)  $y = \sqrt { x + 1 } + 3$ 
B)  $y = \sqrt { x } - 3$ 
C)  $y = \sqrt { x - 1 } - 3$ 
D)  $y = \sqrt { x + 1 } - 3$ 
A)  $y = \sqrt { x + 1 } + 3$ 
B)  $y = \sqrt { x } - 3$ 
C)  $y = \sqrt { x - 1 } - 3$ 
D)  $y = \sqrt { x + 1 } - 3$

Question 12

Find the specified domain.
-Find the domain of $( f g ) ( x )$ when $f ( x ) = \sqrt { 6 x + 9 }$ and $g ( x ) = \sqrt { 7 x - 9 }$

Accepted Answer

A)  $[ 0 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $\left[ - \frac { 9 } { 7 } , \infty \right)$ 
D)  $\left[ \frac { 9 } { 7 } , \infty \right)$ 
A)  $[ 0 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $\left[ - \frac { 9 } { 7 } , \infty \right)$ 
D)  $\left[ \frac { 9 } { 7 } , \infty \right)$

Question 13

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x).
-$$h ( x ) = \frac { 1 } { x ^ { 2 } - 6 }$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 6 } , g ( x ) = x ^ { 2 } - 6$ 
B)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 6 }$ 
C)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 6$ 
D)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 6$ 
A)  $f ( x ) = \frac { 1 } { 6 } , g ( x ) = x ^ { 2 } - 6$ 
B)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 6 }$ 
C)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 6$ 
D)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 6$

Question 14

Graph the function.
-$$f ( x ) = \llbracket x + 1 \rrbracket$$

Accepted Answer

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

Question 15

Find the center-radius form of the equation of the circle.
-center $( 0,6 )$, radius 10

Accepted Answer

A)  $( x + 6 ) ^ { 2 } + y ^ { 2 } = 100$ 
B)  $( x - 6 ) ^ { 2 } + y ^ { 2 } = 100$ 
C)  $x ^ { 2 } + ( y - 6 ) ^ { 2 } = 100$ 
D)  $x ^ { 2 } + ( y + 6 ) ^ { 2 } = 10$ 
A)  $( x + 6 ) ^ { 2 } + y ^ { 2 } = 100$ 
B)  $( x - 6 ) ^ { 2 } + y ^ { 2 } = 100$ 
C)  $x ^ { 2 } + ( y - 6 ) ^ { 2 } = 100$ 
D)  $x ^ { 2 } + ( y + 6 ) ^ { 2 } = 10$

Question 16

Match the equation with the correct graph.
-$$y + 2 = \frac { 8 } { 3 } ( x - 4 )$$

Accepted Answer

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

Question 17

Graph the function.
-$y=8|\times|-9$

Accepted Answer

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

Question 18

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x).
-$$h ( x ) = ( - 8 x + 9 ) ^ { 9 }$$

Accepted Answer

A)  $f ( x ) = - 8 x ^ { 9 } , g ( x ) = x + 9$ 
B)  $f ( x ) = ( - 8 x ) ^ { 9 } , g ( x ) = 9$ 
C)  $f ( x ) = - 8 x + 9 , g ( x ) = x ^ { 9 }$ 
D)  $f ( x ) = x ^ { 9 } , g ( x ) = - 8 x + 9$ 
A)  $f ( x ) = - 8 x ^ { 9 } , g ( x ) = x + 9$ 
B)  $f ( x ) = ( - 8 x ) ^ { 9 } , g ( x ) = 9$ 
C)  $f ( x ) = - 8 x + 9 , g ( x ) = x ^ { 9 }$ 
D)  $f ( x ) = x ^ { 9 } , g ( x ) = - 8 x + 9$

Question 19

Rewrite the equation so that one side is 0, then replace 0 with y. The graph of the equation for y is shown.
Use a graphing calculator to solve the linear equation.
- 
$ 3 x+1+x=2 x-3 $

Accepted Answer

A)  $ y=2 x+4 ;-2 $ 
B)  $ y=4 x+2 ;-2 $ 
C)  $ y=4 x+2 ; 0 $ 
D)  $ y=2 x+4 ; 0 $ 
A)  $ y=2 x+4 ;-2 $ 
B)  $ y=4 x+2 ;-2 $ 
C)  $ y=4 x+2 ; 0 $ 
D)  $ y=2 x+4 ; 0 $

Question 20

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$$P ( - 8 , - 5 ) , Q ( - 2 , - 1 )$$

Accepted Answer

A)  $( - 10 , - 6 )$ 
B)  $( - 6 , - 4 )$ 
C)  $( - 3 , - 2 )$ 
D)  $( - 5 , - 3 )$ 
A)  $( - 10 , - 6 )$ 
B)  $( - 6 , - 4 )$ 
C)  $( - 3 , - 2 )$ 
D)  $( - 5 , - 3 )$

Give the domain and range of the relation. -

Graph the line described. - $\text { through } ( 0,6 ) ; \mathrm { m } = - \frac { 1 } { 6 }$ $Graph the line described. - \text { through } ( 0,6 ) ; \mathrm { m } = - \frac { 1 } { 6 }$

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

Give the domain and range of the relation. - $y = \frac { 14 } { 4 - x }$

Decide whether the relation defines a function. -

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints $( - 3,4 )$ and $( - 3 , - 4 )$

Graph the circle. - $( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$ $Graph the circle. - ( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$

The graph of y = f(x) is given. Use the graph to find the function value. -Find f(-12).

Graph the line described. -through (1, 9); undefined slope

Decide whether the relation defines a function. -

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ -Select the equation that describes the graph shown. $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } -Select the equation that describes the graph shown.$

Find the specified domain. -Find the domain of $( f g ) ( x )$ when $f ( x ) = \sqrt { 6 x + 9 }$ and $g ( x ) = \sqrt { 7 x - 9 }$

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - $h ( x ) = \frac { 1 } { x ^ { 2 } - 6 }$

Graph the function. - $f ( x ) = \llbracket x + 1 \rrbracket$ $Graph the function. - f ( x ) = \llbracket x + 1 \rrbracket$

Find the center-radius form of the equation of the circle. -center $( 0,6 )$ , radius 10

Match the equation with the correct graph. - $y + 2 = \frac { 8 } { 3 } ( x - 4 )$

Graph the function. - $y=8|\times|-9$ $Graph the function. - y=8|\times|-9$

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - $h ( x ) = ( - 8 x + 9 ) ^ { 9 }$

Rewrite the equation so that one side is 0, then replace 0 with y. The graph of the equation for y is shown. Use a graphing calculator to solve the linear equation. - $3 x+1+x=2 x-3$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $P ( - 8 , - 5 ) , Q ( - 2 , - 1 )$

Review of Basic Concepts

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

Filters

Exam 3: Graphs and Functions

Give the domain and range of the relation. -

Graph the line described. - through (0,6);m=−16\text { through } ( 0,6 ) ; \mathrm { m } = - \frac { 1 } { 6 } through (0,6);m=−61​

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

Give the domain and range of the relation. - y=144−xy = \frac { 14 } { 4 - x }y=4−x14​

Decide whether the relation defines a function. -

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints (−3,4)( - 3,4 )(−3,4) and (−3,−4)( - 3 , - 4 )(−3,−4)

Graph the circle. - (x−3)2+y2=4( x - 3 ) ^ { 2 } + y ^ { 2 } = 4(x−3)2+y2=4

The graph of y = f(x) is given. Use the graph to find the function value. -Find f(-12).

Graph the line described. -through (1, 9); undefined slope

Decide whether the relation defines a function. -

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ -Select the equation that describes the graph shown.

Find the specified domain. -Find the domain of (fg)(x)( f g ) ( x )(fg)(x) when f(x)=6x+9f ( x ) = \sqrt { 6 x + 9 }f(x)=6x+9​ and g(x)=7x−9g ( x ) = \sqrt { 7 x - 9 }g(x)=7x−9​

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - h(x)=1x2−6h ( x ) = \frac { 1 } { x ^ { 2 } - 6 }h(x)=x2−61​

Graph the function. - f(x)=⟦x+1⟧f ( x ) = \llbracket x + 1 \rrbracketf(x)=[[x+1]]

Find the center-radius form of the equation of the circle. -center (0,6)( 0,6 )(0,6) , radius 10

Match the equation with the correct graph. - y+2=83(x−4)y + 2 = \frac { 8 } { 3 } ( x - 4 )y+2=38​(x−4)

Graph the function. - y=8∣×∣−9y=8|\times|-9y=8∣×∣−9

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - h(x)=(−8x+9)9h ( x ) = ( - 8 x + 9 ) ^ { 9 }h(x)=(−8x+9)9

Rewrite the equation so that one side is 0, then replace 0 with y. The graph of the equation for y is shown. Use a graphing calculator to solve the linear equation. - 3x+1+x=2x−3 3 x+1+x=2 x-3 3x+1+x=2x−3

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(−8,−5),Q(−2,−1)P ( - 8 , - 5 ) , Q ( - 2 , - 1 )P(−8,−5),Q(−2,−1)

Review of Basic Concepts

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

Filters

Graph the line described. - $\text { through } ( 0,6 ) ; \mathrm { m } = - \frac { 1 } { 6 }$ $Graph the line described. - \text { through } ( 0,6 ) ; \mathrm { m } = - \frac { 1 } { 6 }$

Give the domain and range of the relation. - $y = \frac { 14 } { 4 - x }$

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints $( - 3,4 )$ and $( - 3 , - 4 )$

Graph the circle. - $( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$ $Graph the circle. - ( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ -Select the equation that describes the graph shown. $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } -Select the equation that describes the graph shown.$

Find the specified domain. -Find the domain of $( f g ) ( x )$ when $f ( x ) = \sqrt { 6 x + 9 }$ and $g ( x ) = \sqrt { 7 x - 9 }$

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - $h ( x ) = \frac { 1 } { x ^ { 2 } - 6 }$

Graph the function. - $f ( x ) = \llbracket x + 1 \rrbracket$ $Graph the function. - f ( x ) = \llbracket x + 1 \rrbracket$

Find the center-radius form of the equation of the circle. -center $( 0,6 )$ , radius 10

Match the equation with the correct graph. - $y + 2 = \frac { 8 } { 3 } ( x - 4 )$

Graph the function. - $y=8|\times|-9$ $Graph the function. - y=8|\times|-9$

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - $h ( x ) = ( - 8 x + 9 ) ^ { 9 }$

Rewrite the equation so that one side is 0, then replace 0 with y. The graph of the equation for y is shown. Use a graphing calculator to solve the linear equation. - $3 x+1+x=2 x-3$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $P ( - 8 , - 5 ) , Q ( - 2 , - 1 )$