Question 1

Give the domain and range of the relation.
-$$y = 6 x - 2$$

Accepted Answer

A)  domain: $[ 0 , \infty )$; range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $[ - 2 , \infty )$ 
D)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
A)  domain: $[ 0 , \infty )$; range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $[ - 2 , \infty )$ 
D)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$

Question 2

Provide an appropriate response.
-If the point (a, b) is in the fourth quadrant, in what quadrant is (-a, -b)?

Accepted Answer

A)  I 
B)  II 
C)  III 
D)  IV 
A)  I 
B)  II 
C)  III 
D)  IV

Question 3

Graph the function.
-$$f ( x ) = ( x + 2 ) ^ { 3 } - 3$$

Accepted Answer

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

Question 4

Give the domain and range of the relation.
-$\{ ( 2,7 ) , ( - 1 , - 9 ) , ( - 6 , - 4 ) , ( 6,0 ) \}$

Accepted Answer

A)  domain: $\{ - 9 , - 6 , - 4 , - 1 \}$; range: $\{ 2,6,7 \}$ 
B)  domain: $\{ - 6 , - 1,2,6 \}$; range: $\{ - 9 , - 4,0,7 \}$ 
C)  domain: $\{ - 9 , - 4,0,7 \}$; range: $\{ - 6 , - 1,2,6 \}$ 
D)  domain: $\{ 2,6,7 \}$; range: $\{ - 9 , - 6 , - 4 , - 1 \}$ 
A)  domain: $\{ - 9 , - 6 , - 4 , - 1 \}$; range: $\{ 2,6,7 \}$ 
B)  domain: $\{ - 6 , - 1,2,6 \}$; range: $\{ - 9 , - 4,0,7 \}$ 
C)  domain: $\{ - 9 , - 4,0,7 \}$; range: $\{ - 6 , - 1,2,6 \}$ 
D)  domain: $\{ 2,6,7 \}$; range: $\{ - 9 , - 6 , - 4 , - 1 \}$

Question 5

Evaluate the function.
-Find $f ( k - 1 )$ when $f ( x ) = 5 x ^ { 2 } + 4 x + 2$

Accepted Answer

A)  $5 k ^ { 2 } - 6 k + 11$ 
B)  $5 \mathrm { k } ^ { 2 } + 14 \mathrm { k } + 11$ 
C)  $5 k ^ { 2 } - 6 k + 3$ 
D)  $- 6 k ^ { 2 } + 5 k + 3$ 
A)  $5 k ^ { 2 } - 6 k + 11$ 
B)  $5 \mathrm { k } ^ { 2 } + 14 \mathrm { k } + 11$ 
C)  $5 k ^ { 2 } - 6 k + 3$ 
D)  $- 6 k ^ { 2 } + 5 k + 3$

Question 6

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

Accepted Answer

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

Question 7

Graph the function.
-$$f ( x ) = - \frac { 1 } { 6 } x ^ { 2 }$$

Accepted Answer

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

Question 8

Evaluate the function.
-Find $f ( 4 )$

Accepted Answer

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

Question 9

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
-$$f ( x ) = \frac { 1 } { 4 } x - 3$$

Accepted Answer

A)  $D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
A)  $D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$

Question 10

For the points P and Q, find the distance d(P, Q).
-$$\mathrm { P } ( 9 \sqrt { 11 } , - 2 \sqrt { 7 } ) , \mathrm { Q } ( - 3 \sqrt { 11 } , - 7 \sqrt { 7 } )$$

Accepted Answer

A)  $\sqrt { 1759 }$ 
B)  1759 
C)  $\sqrt { 167 }$ 
D)  167 
A)  $\sqrt { 1759 }$ 
B)  1759 
C)  $\sqrt { 167 }$ 
D)  167

Question 11

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.
-$$y = f ( x ) + 6$$

Accepted Answer

A)  $( - 4,4 )$ 
B)  $( 2,10 )$ 
C)  $( 8,4 )$ 
D)  $( 2 , - 6 )$ 
A)  $( - 4,4 )$ 
B)  $( 2,10 )$ 
C)  $( 8,4 )$ 
D)  $( 2 , - 6 )$

Question 12

Find the average rate of change illustrated in the graph.
-An investment is worth $3578 in year 0, the initial investment year. By year 4 its value has increased to $4262. Let y be the value of the investment in the year x. Find and interpret the
Average rate of change in value per year.

Accepted Answer

A)  $3578 per year; the value of the investment increases by $3578 per year during these years. 
B)  $171 per year; the value of the investment increases by $171 per year during these years. 
C)  $4946 per year; the value of the investment increases by $4946 per year during these years. 
D)  -$171 per year; the value of the investment decreases by $171 per year during these years. 
A)  $3578 per year; the value of the investment increases by $3578 per year during these years. 
B)  $171 per year; the value of the investment increases by $171 per year during these years. 
C)  $4946 per year; the value of the investment increases by $4946 per year during these years. 
D)  -$171 per year; the value of the investment decreases by $171 per year during these years.

Question 13

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

Question 14

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

Accepted Answer

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

Question 15

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
-The radius $\mathrm { r }$ of a circle of known area $\mathrm { A }$ is given by $\mathrm { r } = \sqrt { \mathrm { A } / \pi }$, where $\pi \approx 3.1416$. Find the radius and circumference of a circle with an area of $45.17 \mathrm { sq } \mathrm { ft }$. (Round results to two decimal places.)

Accepted Answer

A)  $\mathrm { r } = 3.79 \mathrm { ft } , \mathrm { C } = 8.86 \mathrm { ft }$ 
B)  $\mathrm { r } = 14.36 \mathrm { ft } , \mathrm { C } = 90.23 \mathrm { ft }$ 
C)  $r = 3.79 \mathrm { ft } , \mathrm { C } = 23.81 \mathrm { sq } \mathrm { ft }$ 
D)  $\mathrm { r } = 3.79 \mathrm { ft } , \mathrm { C } = 23.81 \mathrm { ft }$ 
A)  $\mathrm { r } = 3.79 \mathrm { ft } , \mathrm { C } = 8.86 \mathrm { ft }$ 
B)  $\mathrm { r } = 14.36 \mathrm { ft } , \mathrm { C } = 90.23 \mathrm { ft }$ 
C)  $r = 3.79 \mathrm { ft } , \mathrm { C } = 23.81 \mathrm { sq } \mathrm { ft }$ 
D)  $\mathrm { r } = 3.79 \mathrm { ft } , \mathrm { C } = 23.81 \mathrm { ft }$

Question 16

Give the domain and range of the relation.
-$\{ ( 1,9 ) , ( - 2 , - 8 ) , ( - 6 , - 5 ) , ( 6 , - 8 ) \}$

Accepted Answer

A)  domain: $\{ 1,6,9 \}$; range: $\{ - 8 , - 6 , - 5 , - 2 \}$ 
B)  domain: $\{ - 6 , - 2,1,6 \}$; range: $\{ - 8 , - 5,9 \}$ 
C)  domain: $\{ - 8 , - 5,9 \}$; range: $\{ - 6 , - 2,1,6 \}$ 
D)  domain: $\{ - 8 , - 6 , - 5 , - 2 \}$; range: $\{ 1,6,9 \}$ 
A)  domain: $\{ 1,6,9 \}$; range: $\{ - 8 , - 6 , - 5 , - 2 \}$ 
B)  domain: $\{ - 6 , - 2,1,6 \}$; range: $\{ - 8 , - 5,9 \}$ 
C)  domain: $\{ - 8 , - 5,9 \}$; range: $\{ - 6 , - 2,1,6 \}$ 
D)  domain: $\{ - 8 , - 6 , - 5 , - 2 \}$; range: $\{ 1,6,9 \}$

Question 17

Graph the point symmetric to the given point.
-$$\text { Plot the point } ( 6,0 ) \text {, then plot the point that is symmetric to } ( 6,0 ) \text { with respect to the origin. }$$

Accepted Answer

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

Question 18

Write an equation for the line described. Give your answer in slope-intercept form.
-through $( 7 , - 7 )$ and $( 0 , - 5 )$

Accepted Answer

A)  $y = \frac { 2 } { 7 } x - 5$ 
B)  $y = \frac { 14 } { 5 } x - 5$ 
C)  $y = - \frac { 2 } { 7 } x - 5$ 
D)  $y = - \frac { 14 } { 5 } x - 5$ 
A)  $y = \frac { 2 } { 7 } x - 5$ 
B)  $y = \frac { 14 } { 5 } x - 5$ 
C)  $y = - \frac { 2 } { 7 } x - 5$ 
D)  $y = - \frac { 14 } { 5 } x - 5$

Question 19

Find the slope of the line satisfying the given conditions.
-through $( 6 , - 2 )$ and $( 4,7 )$

Accepted Answer

A)  $\frac { 2 } { 9 }$ 
B)  $- \frac { 2 } { 9 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $- \frac { 9 } { 2 }$ 
A)  $\frac { 2 } { 9 }$ 
B)  $- \frac { 2 } { 9 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $- \frac { 9 } { 2 }$

Question 20

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x).
-$$x + 3 y = 4$$

Accepted Answer

A)  $f ( x ) = - \frac { 1 } { 3 } x + \frac { 4 } { 3 }$ 
B)  $f ( x ) = 3 x - 4$ 
C)  $f ( x ) = - x + \frac { 4 } { 3 }$ 
D)  $f ( x ) = \frac { 1 } { 3 } x + \frac { 4 } { 3 }$ 
A)  $f ( x ) = - \frac { 1 } { 3 } x + \frac { 4 } { 3 }$ 
B)  $f ( x ) = 3 x - 4$ 
C)  $f ( x ) = - x + \frac { 4 } { 3 }$ 
D)  $f ( x ) = \frac { 1 } { 3 } x + \frac { 4 } { 3 }$

Give the domain and range of the relation. - $y = 6 x - 2$

Provide an appropriate response. -If the point (a, b) is in the fourth quadrant, in what quadrant is (-a, -b)?

Graph the function. - $f ( x ) = ( x + 2 ) ^ { 3 } - 3$ $Graph the function. - f ( x ) = ( x + 2 ) ^ { 3 } - 3$

Give the domain and range of the relation. - $\{ ( 2,7 ) , ( - 1 , - 9 ) , ( - 6 , - 4 ) , ( 6,0 ) \}$

Evaluate the function. -Find $f ( k - 1 )$ when $f ( x ) = 5 x ^ { 2 } + 4 x + 2$

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

Graph the function. - $f ( x ) = - \frac { 1 } { 6 } x ^ { 2 }$ $Graph the function. - f ( x ) = - \frac { 1 } { 6 } x ^ { 2 }$

Evaluate the function. -Find $f ( 4 )$

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( 9 \sqrt { 11 } , - 2 \sqrt { 7 } ) , \mathrm { Q } ( - 3 \sqrt { 11 } , - 7 \sqrt { 7 } )$

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - $y = f ( x ) + 6$

Find the average rate of change illustrated in the graph. -An investment is worth $3578 in year 0, the initial investment year. By year 4 its value has increased to $4262. Let y be the value of the investment in the year x. Find and interpret the Average rate of change in value per year.

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

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

Give the domain and range of the relation. - $\{ ( 1,9 ) , ( - 2 , - 8 ) , ( - 6 , - 5 ) , ( 6 , - 8 ) \}$

Write an equation for the line described. Give your answer in slope-intercept form. -through $( 7 , - 7 )$ and $( 0 , - 5 )$

Find the slope of the line satisfying the given conditions. -through $( 6 , - 2 )$ and $( 4,7 )$

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $x + 3 y = 4$

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. - y=6x−2y = 6 x - 2y=6x−2

Provide an appropriate response. -If the point (a, b) is in the fourth quadrant, in what quadrant is (-a, -b)?

Graph the function. - f(x)=(x+2)3−3f ( x ) = ( x + 2 ) ^ { 3 } - 3f(x)=(x+2)3−3

Give the domain and range of the relation. - {(2,7),(−1,−9),(−6,−4),(6,0)}\{ ( 2,7 ) , ( - 1 , - 9 ) , ( - 6 , - 4 ) , ( 6,0 ) \}{(2,7),(−1,−9),(−6,−4),(6,0)}

Evaluate the function. -Find f(k−1)f ( k - 1 )f(k−1) when f(x)=5x2+4x+2f ( x ) = 5 x ^ { 2 } + 4 x + 2f(x)=5x2+4x+2

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

Graph the function. - f(x)=−16x2f ( x ) = - \frac { 1 } { 6 } x ^ { 2 }f(x)=−61​x2

Evaluate the function. -Find f(4)f ( 4 )f(4)

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - f(x)=14x−3f ( x ) = \frac { 1 } { 4 } x - 3f(x)=41​x−3

For the points P and Q, find the distance d(P, Q). - P(911,−27),Q(−311,−77)\mathrm { P } ( 9 \sqrt { 11 } , - 2 \sqrt { 7 } ) , \mathrm { Q } ( - 3 \sqrt { 11 } , - 7 \sqrt { 7 } )P(911​,−27​),Q(−311​,−77​)

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - y=f(x)+6y = f ( x ) + 6y=f(x)+6

Find the average rate of change illustrated in the graph. -An investment is worth $3578 in year 0, the initial investment year. By year 4 its value has increased to $4262. Let y be the value of the investment in the year x. Find and interpret the Average rate of change in value per year.

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

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

Give the domain and range of the relation. - {(1,9),(−2,−8),(−6,−5),(6,−8)}\{ ( 1,9 ) , ( - 2 , - 8 ) , ( - 6 , - 5 ) , ( 6 , - 8 ) \}{(1,9),(−2,−8),(−6,−5),(6,−8)}

Write an equation for the line described. Give your answer in slope-intercept form. -through (7,−7)( 7 , - 7 )(7,−7) and (0,−5)( 0 , - 5 )(0,−5)

Find the slope of the line satisfying the given conditions. -through (6,−2)( 6 , - 2 )(6,−2) and (4,7)( 4,7 )(4,7)

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - x+3y=4x + 3 y = 4x+3y=4

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

Give the domain and range of the relation. - $y = 6 x - 2$

Graph the function. - $f ( x ) = ( x + 2 ) ^ { 3 } - 3$ $Graph the function. - f ( x ) = ( x + 2 ) ^ { 3 } - 3$

Give the domain and range of the relation. - $\{ ( 2,7 ) , ( - 1 , - 9 ) , ( - 6 , - 4 ) , ( 6,0 ) \}$

Evaluate the function. -Find $f ( k - 1 )$ when $f ( x ) = 5 x ^ { 2 } + 4 x + 2$

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

Graph the function. - $f ( x ) = - \frac { 1 } { 6 } x ^ { 2 }$ $Graph the function. - f ( x ) = - \frac { 1 } { 6 } x ^ { 2 }$

Evaluate the function. -Find $f ( 4 )$

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( 9 \sqrt { 11 } , - 2 \sqrt { 7 } ) , \mathrm { Q } ( - 3 \sqrt { 11 } , - 7 \sqrt { 7 } )$

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - $y = f ( x ) + 6$

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

Give the domain and range of the relation. - $\{ ( 1,9 ) , ( - 2 , - 8 ) , ( - 6 , - 5 ) , ( 6 , - 8 ) \}$

Write an equation for the line described. Give your answer in slope-intercept form. -through $( 7 , - 7 )$ and $( 0 , - 5 )$

Find the slope of the line satisfying the given conditions. -through $( 6 , - 2 )$ and $( 4,7 )$

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $x + 3 y = 4$