Question 1

Determine whether $$( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$$
-f(x) = 1x , g(x) = x

Accepted Answer

A)  Yes, yes 
B)  Yes, no 
C)  No, no 
D)  No, yes 
A)  Yes, yes 
B)  Yes, no 
C)  No, no 
D)  No, yes

Question 2

The graph of y = f(x) is given. Use the graph to find the function value.
- 
Find $f ( 4 )$.

Accepted Answer

A)  None of these 
B)  $- 1$ 
C)  4 
D)  15 
A)  None of these 
B)  $- 1$ 
C)  4 
D)  15

Question 3

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 4

Give the domain and range of the relation.
-

Accepted Answer

A)  range: $( - \infty , 0 ) \cup ( 0,4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5,0 ) \cup ( 0 , \infty )$ 
B)  range: $( - \infty , 4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
C)  range: $( - \infty , \infty )$; domain: $( - \infty , \infty )$ 
D)  None of these 
A)  range: $( - \infty , 0 ) \cup ( 0,4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5,0 ) \cup ( 0 , \infty )$ 
B)  range: $( - \infty , 4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
C)  range: $( - \infty , \infty )$; domain: $( - \infty , \infty )$ 
D)  None of these

Question 5

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint $( 3,1 )$, endpoint $( 2 , - 3 )$

Accepted Answer

A)  $( 0 , - 11 )$ 
B)  $( 10 , - 1 )$ 
C)  $( 4,5 )$ 
D)  $( 4 , - 7 )$ 
A)  $( 0 , - 11 )$ 
B)  $( 10 , - 1 )$ 
C)  $( 4,5 )$ 
D)  $( 4 , - 7 )$

Question 6

Find the average rate of change illustrated in the graph.
-A lumber yard has fixed costs of $1702.80 per day and variable costs of $0.48 per board-foot produced. Lumber sells for $1.58 per board-foot. How many board-feet must be produced and sold daily to break even?

Accepted Answer

A)  1548 board-feet 
B)  1032 board-feet 
C)  826 board-feet 
D)  3547 board-feet 
A)  1548 board-feet 
B)  1032 board-feet 
C)  826 board-feet 
D)  3547 board-feet

Question 7

Graph the point symmetric to the given point.
-$$\text { Plot the point } ( - 6 , - 9 ) \text {, then plot the point that is symmetric to } ( - 6 , - 9 ) \text { with respect to the } x - a x i s .$$

Accepted Answer

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

Question 8

Give the domain and range of the relation.
-$$\{ ( 3,7 ) , ( - 1 , - 8 ) , ( - 7 , - 4 ) , ( 5 , - 8 ) \}$$

Accepted Answer

A)  domain: $\{ - 8 , - 7 , - 4 , - 1 \}$; range: $\{ 3,5,7 \}$ 
B)  domain: $\{ - 7 , - 1,3,5 \}$; range: $\{ - 8 , - 4,7 \}$ 
C)  domain: $\{ 3,5,7 \}$; range: $\{ - 8 , - 7 , - 4 , - 1 \}$ 
D)  domain: $\{ - 8 , - 4,7 \}$; range: $\{ - 7 , - 1,3,5 \}$ 
A)  domain: $\{ - 8 , - 7 , - 4 , - 1 \}$; range: $\{ 3,5,7 \}$ 
B)  domain: $\{ - 7 , - 1,3,5 \}$; range: $\{ - 8 , - 4,7 \}$ 
C)  domain: $\{ 3,5,7 \}$; range: $\{ - 8 , - 7 , - 4 , - 1 \}$ 
D)  domain: $\{ - 8 , - 4,7 \}$; range: $\{ - 7 , - 1,3,5 \}$

Question 9

Describe the transformations and give the equation for the graph.
-

Accepted Answer

A)  It is the graph of $f ( x ) = | x |$ shrunken vertically by a factor of 9 and translated 2 units down. The equation is $y = 9 | x | + 2$ 
B)  It is the graph of $f ( x ) = | x |$ stretched vertically by a factor of 9 and translated 2 units down. The equation is $y = 9 | x | - 2$ 
C)  It is the graph of $f ( x ) = | x |$ shrunken vertically by a factor of 9 and translated 2 units down. The equation is $y = \frac { 1 } { 9 } | x | - 2$ 
D)  It is the graph of $f ( x ) = | x |$ stretched vertically by a factor of 9 and translated 2 units down. The equation is $y = \frac { 1 } { 9 } | x | + 2$ 
A)  It is the graph of $f ( x ) = | x |$ shrunken vertically by a factor of 9 and translated 2 units down. The equation is $y = 9 | x | + 2$ 
B)  It is the graph of $f ( x ) = | x |$ stretched vertically by a factor of 9 and translated 2 units down. The equation is $y = 9 | x | - 2$ 
C)  It is the graph of $f ( x ) = | x |$ shrunken vertically by a factor of 9 and translated 2 units down. The equation is $y = \frac { 1 } { 9 } | x | - 2$ 
D)  It is the graph of $f ( x ) = | x |$ stretched vertically by a factor of 9 and translated 2 units down. The equation is $y = \frac { 1 } { 9 } | x | + 2$

Question 10

Find the requested value.
-$$f ( x ) = \left\{ \begin{array} { l l } 
x - 4 , & \text { if } x > 0 \
- 5 , & \text { if } x \leq 0
\end{array} \right.$$

Accepted Answer

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

Question 11

Use the tables to find $( f + g ) ( 2 )$.

Accepted Answer

A)  2 
B)  $- 3$ 
C)  18 
D)  8 
A)  2 
B)  $- 3$ 
C)  18 
D)  8

Question 12

Decide whether the relation defines a function.
-$\{ ( - 8,2 ) , ( - 8,8 ) , ( 1,7 ) , ( 3,6 ) , ( 8,4 ) \}$

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Write an equation for the line described. Give your answer in standard form.
-$x$-intercept $( 2,0 )$, y-intercept $( 0,5 )$

Accepted Answer

A)  $5 x + 2 y = - 10$ 
B)  $- 5 x + 2 y = 10$ 
C)  $5 x - 2 y = 10$ 
D)  $5 x + 2 y = 10$ 
A)  $5 x + 2 y = - 10$ 
B)  $- 5 x + 2 y = 10$ 
C)  $5 x - 2 y = 10$ 
D)  $5 x + 2 y = 10$

Question 15

The graphs of functions $f$ and $g$ are shown. Use these graphs to find $( f + g ) ( 4 )$.

$y = f ( x )$
$y = g ( x )$

Accepted Answer

A)  $- 2$ 
B)  8 
C)  6 
D)  $\frac { 1 } { 2 }$ 
A)  $- 2$ 
B)  8 
C)  6 
D)  $\frac { 1 } { 2 }$

Question 16

Graph the equation by determining the missing values needed to plot the ordered pairs.
-$$y + x = 3 ; ( 2 , \quad ) , ( 3 , \quad ) , ( 1 , \quad )$$

Accepted Answer

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

Question 17

Describe how the graph of the equation relates to the graph $$y = x ^ { 2 }$$
-$f ( x ) = 6 x ^ { 2 }$

Accepted Answer

A)  a translation 6 units to the right 
B)  a horizontal stretch by a factor of 6 
C)  a translation 6 units up 
D)  a vertical stretch by a factor of 6 
A)  a translation 6 units to the right 
B)  a horizontal stretch by a factor of 6 
C)  a translation 6 units up 
D)  a vertical stretch by a factor of 6

Question 18

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$
-$$f ( x ) = \frac { x } { 8 - x }$$

Accepted Answer

A)  $\frac { 8 } { ( 8 - x - h ) ( 8 - x ) }$ 
B)  $ - \frac { 8 } { ( 8 - x + h ) ( 8 - x ) }$ 
C)  $\frac { h x } { ( 8 - x - h ) ( 8 + x ) }$ 
D)  $\frac { x } { ( 8 - x + h ) ( 8 - x ) }$ 
A)  $\frac { 8 } { ( 8 - x - h ) ( 8 - x ) }$ 
B)  $ - \frac { 8 } { ( 8 - x + h ) ( 8 - x ) }$ 
C)  $\frac { h x } { ( 8 - x - h ) ( 8 + x ) }$ 
D)  $\frac { x } { ( 8 - x + h ) ( 8 - x ) }$

Question 19

Find the slope of the line and sketch the graph.
-$2 x+5 y=24$

Accepted Answer

A)  $m = - \frac { 5 } { 2 }$
  
B)  $\mathrm { m } = \frac { 5 } { 2 }$
  
C)  $m = \frac { 2 } { 5 }$
  
D)  $m = - \frac { 2 } { 5 }$
  
A)  $m = - \frac { 5 } { 2 }$
  
B)  $\mathrm { m } = \frac { 5 } { 2 }$
  
C)  $m = \frac { 2 } { 5 }$
  
D)  $m = - \frac { 2 } { 5 }$

Question 20

Graph the line and give the domain and the range.
-$5 x-20 y=0$

Accepted Answer

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

Determine whether $( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$ -f(x) = 1x , g(x) = x

The graph of y = f(x) is given. Use the graph to find the function value. - Find $f ( 4 )$ .

Give the domain and range of the relation. -

Give the domain and range of the relation. -

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint $( 3,1 )$ , endpoint $( 2 , - 3 )$

Find the average rate of change illustrated in the graph. -A lumber yard has fixed costs of $1702.80 per day and variable costs of $0.48 per board-foot produced. Lumber sells for $1.58 per board-foot. How many board-feet must be produced and sold daily to break even?

Give the domain and range of the relation. - $\{ ( 3,7 ) , ( - 1 , - 8 ) , ( - 7 , - 4 ) , ( 5 , - 8 ) \}$

Describe the transformations and give the equation for the graph. -

Use the tables to find $( f + g ) ( 2 )$ .

Decide whether the relation defines a function. - $\{ ( - 8,2 ) , ( - 8,8 ) , ( 1,7 ) , ( 3,6 ) , ( 8,4 ) \}$

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

Write an equation for the line described. Give your answer in standard form. - $x$ -intercept $( 2,0 )$ , y-intercept $( 0,5 )$

The graphs of functions $f$ and $g$ are shown. Use these graphs to find $( f + g ) ( 4 )$ . $y = f ( x )$ $y = g ( x )$

Graph the equation by determining the missing values needed to plot the ordered pairs. - $y + x = 3 ; ( 2 , \quad ) , ( 3 , \quad ) , ( 1 , \quad )$ $Graph the equation by determining the missing values needed to plot the ordered pairs. - y + x = 3 ; ( 2 , \quad ) , ( 3 , \quad ) , ( 1 , \quad )$

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = 6 x ^ { 2 }$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { x } { 8 - x }$

Find the slope of the line and sketch the graph. - $2 x+5 y=24$

Graph the line and give the domain and the range. - $5 x-20 y=0$

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

Determine whether (f∘g)(x)=x and whether (g∘f)(x)=x. ( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }(f∘g)(x)=x and whether (g∘f)(x)=x. -f(x) = 1x , g(x) = x

The graph of y = f(x) is given. Use the graph to find the function value. - Find f(4)f ( 4 )f(4) .

Give the domain and range of the relation. -

Give the domain and range of the relation. -

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (3,1)( 3,1 )(3,1) , endpoint (2,−3)( 2 , - 3 )(2,−3)

Find the average rate of change illustrated in the graph. -A lumber yard has fixed costs of $1702.80 per day and variable costs of $0.48 per board-foot produced. Lumber sells for $1.58 per board-foot. How many board-feet must be produced and sold daily to break even?

Give the domain and range of the relation. - {(3,7),(−1,−8),(−7,−4),(5,−8)}\{ ( 3,7 ) , ( - 1 , - 8 ) , ( - 7 , - 4 ) , ( 5 , - 8 ) \}{(3,7),(−1,−8),(−7,−4),(5,−8)}

Describe the transformations and give the equation for the graph. -

Find the requested value. - f(x)={x−4, if x>0−5, if x≤0f ( x ) = \left\{ \begin{array} { l l } x - 4 , & \text { if } x > 0 \\- 5 , & \text { if } x \leq 0\end{array} \right.f(x)={x−4,−5,​ if x>0 if x≤0​

Use the tables to find (f+g)(2)( f + g ) ( 2 )(f+g)(2) .

Decide whether the relation defines a function. - {(−8,2),(−8,8),(1,7),(3,6),(8,4)}\{ ( - 8,2 ) , ( - 8,8 ) , ( 1,7 ) , ( 3,6 ) , ( 8,4 ) \}{(−8,2),(−8,8),(1,7),(3,6),(8,4)}

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

Write an equation for the line described. Give your answer in standard form. - xxx -intercept (2,0)( 2,0 )(2,0) , y-intercept (0,5)( 0,5 )(0,5)

The graphs of functions fff and ggg are shown. Use these graphs to find (f+g)(4)( f + g ) ( 4 )(f+g)(4) . y=f(x)y = f ( x )y=f(x) y=g(x)y = g ( x )y=g(x)

Graph the equation by determining the missing values needed to plot the ordered pairs. - y+x=3;(2,),(3,),(1,)y + x = 3 ; ( 2 , \quad ) , ( 3 , \quad ) , ( 1 , \quad )y+x=3;(2,),(3,),(1,)

Describe how the graph of the equation relates to the graph y=x2y = x ^ { 2 }y=x2 - f(x)=6x2f ( x ) = 6 x ^ { 2 }f(x)=6x2

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)=x8−xf ( x ) = \frac { x } { 8 - x }f(x)=8−xx​

Find the slope of the line and sketch the graph. - 2x+5y=242 x+5 y=242x+5y=24

Graph the line and give the domain and the range. - 5x−20y=05 x-20 y=05x−20y=0

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

Determine whether $( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$ -f(x) = 1x , g(x) = x

The graph of y = f(x) is given. Use the graph to find the function value. - Find $f ( 4 )$ .

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint $( 3,1 )$ , endpoint $( 2 , - 3 )$

Give the domain and range of the relation. - $\{ ( 3,7 ) , ( - 1 , - 8 ) , ( - 7 , - 4 ) , ( 5 , - 8 ) \}$

Use the tables to find $( f + g ) ( 2 )$ .

Decide whether the relation defines a function. - $\{ ( - 8,2 ) , ( - 8,8 ) , ( 1,7 ) , ( 3,6 ) , ( 8,4 ) \}$

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

Write an equation for the line described. Give your answer in standard form. - $x$ -intercept $( 2,0 )$ , y-intercept $( 0,5 )$

The graphs of functions $f$ and $g$ are shown. Use these graphs to find $( f + g ) ( 4 )$ . $y = f ( x )$ $y = g ( x )$

Graph the equation by determining the missing values needed to plot the ordered pairs. - $y + x = 3 ; ( 2 , \quad ) , ( 3 , \quad ) , ( 1 , \quad )$ $Graph the equation by determining the missing values needed to plot the ordered pairs. - y + x = 3 ; ( 2 , \quad ) , ( 3 , \quad ) , ( 1 , \quad )$

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = 6 x ^ { 2 }$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { x } { 8 - x }$

Find the slope of the line and sketch the graph. - $2 x+5 y=24$

Graph the line and give the domain and the range. - $5 x-20 y=0$