Question 1

Give the domain and range of the relation.
-$$\{ ( 2,2 ) , ( - 1 , - 1 ) , ( - 6 , - 6 ) , ( 5,5 ) \}$$

Accepted Answer

A)  domain: $\{ - 6 , - 1,2,5 \}$; range: $\{ - 6 , - 1,2,5 \}$ 
B)  domain: $\{ 2,5 \}$; range: $\{ - 6 , - 1 \}$ 
C)  None of these 
D)  domain: $\{ - 6 , - 1 \}$; range: $\{ 2,5 \}$ 
A)  domain: $\{ - 6 , - 1,2,5 \}$; range: $\{ - 6 , - 1,2,5 \}$ 
B)  domain: $\{ 2,5 \}$; range: $\{ - 6 , - 1 \}$ 
C)  None of these 
D)  domain: $\{ - 6 , - 1 \}$; range: $\{ 2,5 \}$

Question 2

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 3

Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of
these.
-$$y = ( x - 9 ) ( x + 8 )$$

Accepted Answer

A)  $y$-axis only 
B)  none of these 
C)  $x$-axis only 
D)  $x$-axis, $y$-axis, origin 
A)  $y$-axis only 
B)  none of these 
C)  $x$-axis only 
D)  $x$-axis, $y$-axis, origin

Question 4

Use a graphing calculator to solve the linear equation.
-$$10 y = 5 y + 9 + 4 y$$

Accepted Answer

A)  $\{ - 9 \}$ 
B)  $\{ - 90 \}$ 
C)  $\{ 90 \}$ 
D)  $\{ 9 \}$ 
A)  $\{ - 9 \}$ 
B)  $\{ - 90 \}$ 
C)  $\{ 90 \}$ 
D)  $\{ 9 \}$

Question 5

Suppose the point (2, 4) is on the graph of y $y = f ( x )$ . Find a point on the graph of the given function.
-$$y = f ( x ) + 4$$

Accepted Answer

A)  $( - 2,4 )$ 
B)  $( 2 , - 4 )$ 
C)  $( 6,4 )$ 
D)  $( 2,8 )$ 
A)  $( - 2,4 )$ 
B)  $( 2 , - 4 )$ 
C)  $( 6,4 )$ 
D)  $( 2,8 )$

Question 6

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

Accepted Answer

A)  Increasing $( 3 , \infty )$; Decreasing $( - \infty , - 3 )$; Constant $( - 3,3 )$ 
B)  Increasing $( - \infty , 3 )$; Decreasing $( - \infty , - 3 )$; Constant $( - 3,3 )$ 
C)  Increasing $( 3 , \infty )$; Decreasing $( - 3 , \infty )$; Constant $( - 3,3 )$ 
D)  Increasing $( - \infty , 3 )$; Decreasing $( - 3 , \infty )$; Constant $( - 3,3 )$ 
A)  Increasing $( 3 , \infty )$; Decreasing $( - \infty , - 3 )$; Constant $( - 3,3 )$ 
B)  Increasing $( - \infty , 3 )$; Decreasing $( - \infty , - 3 )$; Constant $( - 3,3 )$ 
C)  Increasing $( 3 , \infty )$; Decreasing $( - 3 , \infty )$; Constant $( - 3,3 )$ 
D)  Increasing $( - \infty , 3 )$; Decreasing $( - 3 , \infty )$; Constant $( - 3,3 )$

Question 7

Write all linear equations in slope-intercept form.
-A company can make 9 satellite dishes for $92,300, while 16 satellite dishes cost $97,130. Find a linear equation that models the cost to produce x satellite dishes.

Accepted Answer

A)  $y = 7 x + 4830$ 
B)  $y = 690 x + 86,090$ 
C)  $y = 690 x - 86,090$ 
D)  $y = x + 4830$ 
A)  $y = 7 x + 4830$ 
B)  $y = 690 x + 86,090$ 
C)  $y = 690 x - 86,090$ 
D)  $y = x + 4830$

Question 8

Give the domain and range of the relation.
-$$x y = 10$$

Accepted Answer

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

Question 9

Use the graph to determine the equation of the circle in center-radius form.
-

Accepted Answer

A)  $( x + 1 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 9$ 
B)  $( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 9$ 
C)  $( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 3$ 
D)  $( x + 1 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 3$ 
A)  $( x + 1 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 9$ 
B)  $( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 9$ 
C)  $( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 3$ 
D)  $( x + 1 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 3$

Question 10

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = 9 x ^ { 2 } - 7 x , g ( x ) = x ^ { 2 } - 5 x - 14$$
Find $\left( \frac { f } { g } \right) ( x )$.

Accepted Answer

A)  $\frac { 9 x } { x + 1 }$ 
B)  $\frac { 9 x ^ { 2 } - 7 x } { x ^ { 2 } - 5 x - 14 }$ 
C)  $\frac { 9 x - 7 } { - 5 }$ 
D)  $\frac { 9 - x } { 14 }$ 
A)  $\frac { 9 x } { x + 1 }$ 
B)  $\frac { 9 x ^ { 2 } - 7 x } { x ^ { 2 } - 5 x - 14 }$ 
C)  $\frac { 9 x - 7 } { - 5 }$ 
D)  $\frac { 9 - x } { 14 }$

Question 11

Decide whether the relation defines a function.
-$\{ ( - 5,1 ) , ( - 3 , - 6 ) , ( 3 , - 2 ) , ( 3,3 ) \}$

Accepted Answer

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

Question 12

Determine whether the three points are collinear.
-$$( - 3 , - 7 ) , ( 0 , - 1 ) , ( 6,11 )$$

Accepted Answer

A) True 
 B)False

Question 13

Find the specified domain.
-Find the domain of $( f g ) ( x )$ when $f ( x ) = \sqrt { 7 x + 6 }$ and $g ( x ) = \sqrt { 5 x - 9 }$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $[ 0 , \infty )$ 
C)  $\left[ - \frac { 9 } { 5 } , \infty \right)$ 
D)  $\left[ \frac { 9 } { 5 } , \infty \right]$ 
A)  $( - \infty , \infty )$ 
B)  $[ 0 , \infty )$ 
C)  $\left[ - \frac { 9 } { 5 } , \infty \right)$ 
D)  $\left[ \frac { 9 } { 5 } , \infty \right]$

Question 14

Give the domain and range of the relation.
-$$y = \frac { 7 } { 14 - x }$$

Accepted Answer

A)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  domain: $( - \infty , 14 ) \cup ( 14 , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 14 ) \cup ( 14 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  domain: $( - \infty , 14 ) \cup ( 14 , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 14 ) \cup ( 14 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$

Question 15

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$
-$$f ( x ) = \frac { 13 } { x + 26 }$$

Accepted Answer

A)  $- \frac { 13 } { ( x + 13 ) ^ { 2 } }$ 
B)  $- \frac { 338 } { ( x + h + 26 ) ( x + 26 ) }$ 
C)  $\frac { 13 } { ( x + h + 26 ) ( x + 26 ) }$ 
D)  $- \frac { 13 } { ( x + h + 26 ) ( x + 26 ) }$ 
A)  $- \frac { 13 } { ( x + 13 ) ^ { 2 } }$ 
B)  $- \frac { 338 } { ( x + h + 26 ) ( x + 26 ) }$ 
C)  $\frac { 13 } { ( x + h + 26 ) ( x + 26 ) }$ 
D)  $- \frac { 13 } { ( x + h + 26 ) ( x + 26 ) }$

Question 16

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ .
-$f(x)=(x-3)^{2}$

Accepted Answer

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

Question 17

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ .
-$y=(x+3)^{2}+5$

Accepted Answer

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

Question 18

Evaluate the function.
-Find f(4)

Accepted Answer

A)  7 
B)  (12, 7) 
C)  12 
D)  None of these 
A)  7 
B)  (12, 7) 
C)  12 
D)  None of these

Question 19

Graph the equation by plotting points.
-$y=x^{3}+2$

Accepted Answer

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

Question 20

Determine whether the three points are the vertices of a right triangle.
-$( - 2,3 ) , ( 0,7 ) , ( 2,6 )$

Accepted Answer

A) True 
 B)False

Give the domain and range of the relation. - $\{ ( 2,2 ) , ( - 1 , - 1 ) , ( - 6 , - 6 ) , ( 5,5 ) \}$

Decide whether the relation defines a function. -

Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of these. - $y = ( x - 9 ) ( x + 8 )$

Use a graphing calculator to solve the linear equation. - $10 y = 5 y + 9 + 4 y$

Suppose the point (2, 4) is on the graph of y $y = f ( x )$ . Find a point on the graph of the given function. - $y = f ( x ) + 4$

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

Write all linear equations in slope-intercept form. -A company can make 9 satellite dishes for $92,300, while 16 satellite dishes cost $97,130. Find a linear equation that models the cost to produce x satellite dishes.

Give the domain and range of the relation. - $x y = 10$

Use the graph to determine the equation of the circle in center-radius form. -

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 9 x ^ { 2 } - 7 x , g ( x ) = x ^ { 2 } - 5 x - 14$ Find $\left( \frac { f } { g } \right) ( x )$ .

Decide whether the relation defines a function. - $\{ ( - 5,1 ) , ( - 3 , - 6 ) , ( 3 , - 2 ) , ( 3,3 ) \}$

Determine whether the three points are collinear. - $( - 3 , - 7 ) , ( 0 , - 1 ) , ( 6,11 )$

Find the specified domain. -Find the domain of $( f g ) ( x )$ when $f ( x ) = \sqrt { 7 x + 6 }$ and $g ( x ) = \sqrt { 5 x - 9 }$

Give the domain and range of the relation. - $y = \frac { 7 } { 14 - x }$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { 13 } { x + 26 }$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x)=(x-3)^{2}$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x)=(x-3)^{2}$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $y=(x+3)^{2}+5$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - y=(x+3)^{2}+5$

Evaluate the function. -Find f(4)

Graph the equation by plotting points. - $y=x^{3}+2$ $Graph the equation by plotting points. - y=x^{3}+2$

Determine whether the three points are the vertices of a right triangle. - $( - 2,3 ) , ( 0,7 ) , ( 2,6 )$

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 3: Graphs and Functions

Give the domain and range of the relation. - {(2,2),(−1,−1),(−6,−6),(5,5)}\{ ( 2,2 ) , ( - 1 , - 1 ) , ( - 6 , - 6 ) , ( 5,5 ) \}{(2,2),(−1,−1),(−6,−6),(5,5)}

Decide whether the relation defines a function. -

Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of these. - y=(x−9)(x+8)y = ( x - 9 ) ( x + 8 )y=(x−9)(x+8)

Use a graphing calculator to solve the linear equation. - 10y=5y+9+4y10 y = 5 y + 9 + 4 y10y=5y+9+4y

Suppose the point (2, 4) is on the graph of y y=f(x)y = f ( x )y=f(x) . Find a point on the graph of the given function. - y=f(x)+4y = f ( x ) + 4y=f(x)+4

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

Write all linear equations in slope-intercept form. -A company can make 9 satellite dishes for $92,300, while 16 satellite dishes cost $97,130. Find a linear equation that models the cost to produce x satellite dishes.

Give the domain and range of the relation. - xy=10x y = 10xy=10

Use the graph to determine the equation of the circle in center-radius form. -

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=9x2−7x,g(x)=x2−5x−14f ( x ) = 9 x ^ { 2 } - 7 x , g ( x ) = x ^ { 2 } - 5 x - 14f(x)=9x2−7x,g(x)=x2−5x−14 Find (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x) .

Decide whether the relation defines a function. - {(−5,1),(−3,−6),(3,−2),(3,3)}\{ ( - 5,1 ) , ( - 3 , - 6 ) , ( 3 , - 2 ) , ( 3,3 ) \}{(−5,1),(−3,−6),(3,−2),(3,3)}

Determine whether the three points are collinear. - (−3,−7),(0,−1),(6,11)( - 3 , - 7 ) , ( 0 , - 1 ) , ( 6,11 )(−3,−7),(0,−1),(6,11)

Find the specified domain. -Find the domain of (fg)(x)( f g ) ( x )(fg)(x) when f(x)=7x+6f ( x ) = \sqrt { 7 x + 6 }f(x)=7x+6​ and g(x)=5x−9g ( x ) = \sqrt { 5 x - 9 }g(x)=5x−9​

Give the domain and range of the relation. - y=714−xy = \frac { 7 } { 14 - x }y=14−x7​

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)=13x+26f ( x ) = \frac { 13 } { x + 26 }f(x)=x+2613​

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ . - f(x)=(x−3)2f(x)=(x-3)^{2}f(x)=(x−3)2

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ . - y=(x+3)2+5y=(x+3)^{2}+5y=(x+3)2+5

Evaluate the function. -Find f(4)

Graph the equation by plotting points. - y=x3+2y=x^{3}+2y=x3+2

Determine whether the three points are the vertices of a right triangle. - (−2,3),(0,7),(2,6)( - 2,3 ) , ( 0,7 ) , ( 2,6 )(−2,3),(0,7),(2,6)

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Give the domain and range of the relation. - $\{ ( 2,2 ) , ( - 1 , - 1 ) , ( - 6 , - 6 ) , ( 5,5 ) \}$

Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of these. - $y = ( x - 9 ) ( x + 8 )$

Use a graphing calculator to solve the linear equation. - $10 y = 5 y + 9 + 4 y$

Suppose the point (2, 4) is on the graph of y $y = f ( x )$ . Find a point on the graph of the given function. - $y = f ( x ) + 4$

Give the domain and range of the relation. - $x y = 10$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 9 x ^ { 2 } - 7 x , g ( x ) = x ^ { 2 } - 5 x - 14$ Find $\left( \frac { f } { g } \right) ( x )$ .

Decide whether the relation defines a function. - $\{ ( - 5,1 ) , ( - 3 , - 6 ) , ( 3 , - 2 ) , ( 3,3 ) \}$

Determine whether the three points are collinear. - $( - 3 , - 7 ) , ( 0 , - 1 ) , ( 6,11 )$

Find the specified domain. -Find the domain of $( f g ) ( x )$ when $f ( x ) = \sqrt { 7 x + 6 }$ and $g ( x ) = \sqrt { 5 x - 9 }$

Give the domain and range of the relation. - $y = \frac { 7 } { 14 - x }$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { 13 } { x + 26 }$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x)=(x-3)^{2}$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x)=(x-3)^{2}$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $y=(x+3)^{2}+5$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - y=(x+3)^{2}+5$

Graph the equation by plotting points. - $y=x^{3}+2$ $Graph the equation by plotting points. - y=x^{3}+2$

Determine whether the three points are the vertices of a right triangle. - $( - 2,3 ) , ( 0,7 ) , ( 2,6 )$