Question 1

Find the specified domain.
-Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = \sqrt { 4 x - 6 }$ and $g ( x ) = \frac { 1 } { x }$

Accepted Answer

A)  $\left[ \frac { 3 } { 2 } , \infty \right]$ 
B)  $\left[ - \frac { 3 } { 2 } , \infty \right)$ 
C)  $( \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $\left[ - \frac { 3 } { 2 } , 0 \right] \cup ( 0 , \infty )$ 
A)  $\left[ \frac { 3 } { 2 } , \infty \right]$ 
B)  $\left[ - \frac { 3 } { 2 } , \infty \right)$ 
C)  $( \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $\left[ - \frac { 3 } { 2 } , 0 \right] \cup ( 0 , \infty )$

Question 2

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x).
-$$9 x - 3 y = 7$$

Accepted Answer

A)  $f ( x ) = 3 x - \frac { 7 } { 3 }$ 
B)  $f ( x ) = \frac { 1 } { 3 } x + \frac { 7 } { 9 }$ 
C)  $f ( x ) = 9 x - 7$ 
D)  $f ( x ) = 3 x + \frac { 7 } { 3 }$ 
A)  $f ( x ) = 3 x - \frac { 7 } { 3 }$ 
B)  $f ( x ) = \frac { 1 } { 3 } x + \frac { 7 } { 9 }$ 
C)  $f ( x ) = 9 x - 7$ 
D)  $f ( x ) = 3 x + \frac { 7 } { 3 }$

Question 3

Decide whether the relation defines a function.
-$7 x = 14 - 5 y$

Accepted Answer

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

Question 4

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$x ^ { 2 } + y ^ { 2 } + 16 x - 4 y + 52 = 0$$

Accepted Answer

A)  yes 
B)  no; the graph is nonexistent 
C)  no; the graph is the point $( 8 , - 2 )$ 
D)  no; the graph is the point $( - 8,2 )$ 
A)  yes 
B)  no; the graph is nonexistent 
C)  no; the graph is the point $( 8 , - 2 )$ 
D)  no; the graph is the point $( - 8,2 )$

Question 5

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 6

Graph the equation by plotting points.
-$$y = | x | + 5$$

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Decide whether the relation defines a function.
-{(-6, -4), (-1, 3), (1, 2), (5, -7)}

Accepted Answer

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

Question 9

Give the domain and range of the relation.
-$$\{ ( 3,3 ) , ( - 2 , - 2 ) , ( - 7 , - 7 ) , ( 4,4 ) \}$$

Accepted Answer

A)  domain: $\{ 3,4 \}$; range: $\{ - 7 , - 2 \}$ 
B)  domain: $\{ - 7 , - 2 \}$; range: $\{ 3,4 \}$ 
C)  None of these 
D)  domain: $\{ - 7 , - 2,3,4 \}$; range: $\{ - 7 , - 2,3,4 \}$ 
A)  domain: $\{ 3,4 \}$; range: $\{ - 7 , - 2 \}$ 
B)  domain: $\{ - 7 , - 2 \}$; range: $\{ 3,4 \}$ 
C)  None of these 
D)  domain: $\{ - 7 , - 2,3,4 \}$; range: $\{ - 7 , - 2,3,4 \}$

Question 10

Find the specified domain.
-Find the domain of $( f + g ) ( x )$ when $f ( x ) = 5 x - 10$ and $g ( x ) = \frac { 2 } { x - 5 }$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  $( - \infty , - 5 ) \cup ( - 5 , \infty )$

Question 11

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.
-$$10 y = 7 y + 8 + 2 y$$

Accepted Answer

A)  $\{ - 8 \}$ 
B)  $\{ 80 \}$ 
C)  $\{ 8 \}$ 
D)  $\{ - 80 \}$ 
A)  $\{ - 8 \}$ 
B)  $\{ 80 \}$ 
C)  $\{ 8 \}$ 
D)  $\{ - 80 \}$

Question 12

Graph the equation by determining the missing values needed to plot the ordered pairs.
-$$4 y = - 2 x + 8 ; ( 0 , \quad ) , ( , 0 ) , ( 1 , \quad )$$

Accepted Answer

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

Question 13

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.  
-At what time was the temperature the highest?

Accepted Answer

A)  11 a.m. 
B)  1 p.m. 
C)  2 p.m. 
D)  5 p.m. 
A)  11 a.m. 
B)  1 p.m. 
C)  2 p.m. 
D)  5 p.m.

Question 14

Find the center-radius form of the circle described or graphed.
-Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (0, 7), (-12, 15), and (-8, -9) respectively. The epicenter of an earthquake is determined to be 5 units from
X, 15 units from Y, and 13 units from Z. Where on the coordinate plane is the epicenter located?

Accepted Answer

A)  at (-3, 3) 
B)  at (-2, 2) 
C)  at (-2, 3) 
D)  at (-4, 5) 
A)  at (-3, 3) 
B)  at (-2, 2) 
C)  at (-2, 3) 
D)  at (-4, 5)

Question 15

Write an equation for the line described. Give your answer in slope-intercept form.
-$$m = \frac { 9 } { 4 } , b = - 3$$

Accepted Answer

A)  $y = \frac { 9 } { 4 } x - 3$ 
B)  $y = \frac { 9 } { 4 } x + 3$ 
C)  $y = - 3 x + \frac { 9 } { 4 }$ 
D)  $\frac { 9 } { 4 } x - 3 y = 0$ 
A)  $y = \frac { 9 } { 4 } x - 3$ 
B)  $y = \frac { 9 } { 4 } x + 3$ 
C)  $y = - 3 x + \frac { 9 } { 4 }$ 
D)  $\frac { 9 } { 4 } x - 3 y = 0$

Question 16

Determine the intervals of the domain over which the function is continuous.
-

Accepted Answer

A)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
B)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $[ 0 , \infty ]$ 
A)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
B)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $[ 0 , \infty ]$

Question 17

Find the slope and the y-intercept of the line.
-$$6 x - y = - 5$$

Accepted Answer

A)  slope: $6 ; y$-intercept: $( 0,5 )$ 
B)  slope: 6 ; y-intercept: $( 0 , - 5 )$ 
C)  slope: $\frac { 1 } { 6 } ; y$-intercept: $( 0 , - 5 )$ 
D)  slope: 5 ; y-intercept: $( 0,6 )$ 
A)  slope: $6 ; y$-intercept: $( 0,5 )$ 
B)  slope: 6 ; y-intercept: $( 0 , - 5 )$ 
C)  slope: $\frac { 1 } { 6 } ; y$-intercept: $( 0 , - 5 )$ 
D)  slope: 5 ; y-intercept: $( 0,6 )$

Question 18

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

Accepted Answer

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

Question 19

Describe the transformations and give the equation for the graph.
-Find $( f + g ) ( - 1 )$ when $f ( x ) = x + 5$ and $g ( x ) = x + 4$

Accepted Answer

A)  $- 1$ 
B)  7 
C)  $- 3$ 
D)  $- 11$ 
A)  $- 1$ 
B)  7 
C)  $- 3$ 
D)  $- 11$

Question 20

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)

Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = \sqrt { 4 x - 6 }$ and $g ( x ) = \frac { 1 } { x }$

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $9 x - 3 y = 7$

Decide whether the relation defines a function. - $7 x = 14 - 5 y$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } + 16 x - 4 y + 52 = 0$

Decide whether the relation defines a function. -

Graph the equation by plotting points. - $y = | x | + 5$

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

Decide whether the relation defines a function. -{(-6, -4), (-1, 3), (1, 2), (5, -7)}

Give the domain and range of the relation. - $\{ ( 3,3 ) , ( - 2 , - 2 ) , ( - 7 , - 7 ) , ( 4,4 ) \}$

Find the specified domain. -Find the domain of $( f + g ) ( x )$ when $f ( x ) = 5 x - 10$ and $g ( x ) = \frac { 2 } { x - 5 }$

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. - $10 y = 7 y + 8 + 2 y$

Graph the equation by determining the missing values needed to plot the ordered pairs. - $4 y = - 2 x + 8 ; ( 0 , \quad ) , ( , 0 ) , ( 1 , \quad )$ $Graph the equation by determining the missing values needed to plot the ordered pairs. - 4 y = - 2 x + 8 ; ( 0 , \quad ) , ( , 0 ) , ( 1 , \quad )$

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -At what time was the temperature the highest?

Write an equation for the line described. Give your answer in slope-intercept form. - $m = \frac { 9 } { 4 } , b = - 3$

Determine the intervals of the domain over which the function is continuous. -

Find the slope and the y-intercept of the line. - $6 x - y = - 5$

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

Describe the transformations and give the equation for the graph. -Find $( f + g ) ( - 1 )$ when $f ( x ) = x + 5$ and $g ( x ) = x + 4$

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

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

Find the specified domain. -Find the domain of (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x) when f(x)=4x−6f ( x ) = \sqrt { 4 x - 6 }f(x)=4x−6​ and g(x)=1xg ( x ) = \frac { 1 } { x }g(x)=x1​

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - 9x−3y=79 x - 3 y = 79x−3y=7

Decide whether the relation defines a function. - 7x=14−5y7 x = 14 - 5 y7x=14−5y

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - x2+y2+16x−4y+52=0x ^ { 2 } + y ^ { 2 } + 16 x - 4 y + 52 = 0x2+y2+16x−4y+52=0

Decide whether the relation defines a function. -

Graph the equation by plotting points. - y=∣x∣+5y = | x | + 5y=∣x∣+5

Graph the function. - g(x)=−(x+4)3−2g ( x ) = - ( x + 4 ) ^ { 3 } - 2g(x)=−(x+4)3−2

Decide whether the relation defines a function. -{(-6, -4), (-1, 3), (1, 2), (5, -7)}

Give the domain and range of the relation. - {(3,3),(−2,−2),(−7,−7),(4,4)}\{ ( 3,3 ) , ( - 2 , - 2 ) , ( - 7 , - 7 ) , ( 4,4 ) \}{(3,3),(−2,−2),(−7,−7),(4,4)}

Find the specified domain. -Find the domain of (f+g)(x)( f + g ) ( x )(f+g)(x) when f(x)=5x−10f ( x ) = 5 x - 10f(x)=5x−10 and g(x)=2x−5g ( x ) = \frac { 2 } { x - 5 }g(x)=x−52​

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. - 10y=7y+8+2y10 y = 7 y + 8 + 2 y10y=7y+8+2y

Graph the equation by determining the missing values needed to plot the ordered pairs. - 4y=−2x+8;(0,),(,0),(1,)4 y = - 2 x + 8 ; ( 0 , \quad ) , ( , 0 ) , ( 1 , \quad )4y=−2x+8;(0,),(,0),(1,)

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -At what time was the temperature the highest?

Write an equation for the line described. Give your answer in slope-intercept form. - m=94,b=−3m = \frac { 9 } { 4 } , b = - 3m=49​,b=−3

Determine the intervals of the domain over which the function is continuous. -

Find the slope and the y-intercept of the line. - 6x−y=−56 x - y = - 56x−y=−5

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

Describe the transformations and give the equation for the graph. -Find (f+g)(−1)( f + g ) ( - 1 )(f+g)(−1) when f(x)=x+5f ( x ) = x + 5f(x)=x+5 and g(x)=x+4g ( x ) = x + 4g(x)=x+4

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).

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

Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = \sqrt { 4 x - 6 }$ and $g ( x ) = \frac { 1 } { x }$

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $9 x - 3 y = 7$

Decide whether the relation defines a function. - $7 x = 14 - 5 y$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } + 16 x - 4 y + 52 = 0$

Graph the equation by plotting points. - $y = | x | + 5$

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

Give the domain and range of the relation. - $\{ ( 3,3 ) , ( - 2 , - 2 ) , ( - 7 , - 7 ) , ( 4,4 ) \}$

Find the specified domain. -Find the domain of $( f + g ) ( x )$ when $f ( x ) = 5 x - 10$ and $g ( x ) = \frac { 2 } { x - 5 }$

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. - $10 y = 7 y + 8 + 2 y$

Graph the equation by determining the missing values needed to plot the ordered pairs. - $4 y = - 2 x + 8 ; ( 0 , \quad ) , ( , 0 ) , ( 1 , \quad )$ $Graph the equation by determining the missing values needed to plot the ordered pairs. - 4 y = - 2 x + 8 ; ( 0 , \quad ) , ( , 0 ) , ( 1 , \quad )$

Write an equation for the line described. Give your answer in slope-intercept form. - $m = \frac { 9 } { 4 } , b = - 3$

Find the slope and the y-intercept of the line. - $6 x - y = - 5$

Describe the transformations and give the equation for the graph. -Find $( f + g ) ( - 1 )$ when $f ( x ) = x + 5$ and $g ( x ) = x + 4$

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