Question 1

Find the center-radius form of the circle described or graphed.
-

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Find the requested value.
-$$\text { Using the given tables, find (f } g \text { ) (2) }$$

Accepted Answer

A)  10 
B)  2 
C)  6 
D)  3 
A)  10 
B)  2 
C)  6 
D)  3

Question 4

Find the slope and the y-intercept of the line.
-$$x + 4 y = - 5$$

Accepted Answer

A)  slope: $- \frac { 5 } { 4 } ; \mathrm { y }$-intercept: $\left( 0 , - \frac { 1 } { 4 } \right)$ 
B)  slope: $- \frac { 1 } { 4 } ; y$-intercept: $\left( 0 , - \frac { 5 } { 4 } \right)$ 
C)  slope: $\frac { 1 } { 4 } ; \mathrm { y }$-intercept: $\left( 0 , - \frac { 5 } { 4 } \right)$ 
D)  slope: $- 4 ; \mathrm { y }$-intercept: $( 0 , - 5 )$ 
A)  slope: $- \frac { 5 } { 4 } ; \mathrm { y }$-intercept: $\left( 0 , - \frac { 1 } { 4 } \right)$ 
B)  slope: $- \frac { 1 } { 4 } ; y$-intercept: $\left( 0 , - \frac { 5 } { 4 } \right)$ 
C)  slope: $\frac { 1 } { 4 } ; \mathrm { y }$-intercept: $\left( 0 , - \frac { 5 } { 4 } \right)$ 
D)  slope: $- 4 ; \mathrm { y }$-intercept: $( 0 , - 5 )$

Question 5

Find the center-radius form of the circle described or graphed.
-a circle having a diameter with endpoints $( - 2,3 )$ and $( 8 , - 5 )$

Accepted Answer

A)  $x ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 41$ 
C)  $( x - 3 ) ^ { 2 } + y ^ { 2 } = 16$ 
D)  $( x + 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 41$ 
A)  $x ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 41$ 
C)  $( x - 3 ) ^ { 2 } + y ^ { 2 } = 16$ 
D)  $( x + 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 41$

Question 6

Provide an appropriate response.
-If a horizontal line is drawn through the point $( 1 , - 8 )$, where will it intersect the $y$-axis?

Accepted Answer

A)  $( 1,0 )$ 
B)  $( 0,1 )$ 
C)  $( 0 , - 8 )$ 
D)  $( - 8,0 )$ 
A)  $( 1,0 )$ 
B)  $( 0,1 )$ 
C)  $( 0 , - 8 )$ 
D)  $( - 8,0 )$

Question 7

Give the domain and range of the relation.
-$\{ ( 3,7 ) , ( - 2 , - 9 ) , ( - 6 , - 4 ) , ( 5,0 ) \}$

Accepted Answer

A)  domain: $\{ 3,5,7 \}$; range: $\{ - 9 , - 6 , - 4 , - 2 \}$ 
B)  domain: $\{ - 9 , - 4,0,7 \}$; range: $\{ - 6 , - 2,3,5 \}$ 
C)  domain: $\{ - 9 , - 6 , - 4 , - 2 \}$; range: $\{ 3,5,7 \}$ 
D)  domain: $\{ - 6 , - 2,3,5 \}$; range: $\{ - 9 , - 4,0,7 \}$ 
A)  domain: $\{ 3,5,7 \}$; range: $\{ - 9 , - 6 , - 4 , - 2 \}$ 
B)  domain: $\{ - 9 , - 4,0,7 \}$; range: $\{ - 6 , - 2,3,5 \}$ 
C)  domain: $\{ - 9 , - 6 , - 4 , - 2 \}$; range: $\{ 3,5,7 \}$ 
D)  domain: $\{ - 6 , - 2,3,5 \}$; range: $\{ - 9 , - 4,0,7 \}$

Question 8

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ .
-$f(x)=|x|+4$

Accepted Answer

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

Question 9

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = x ^ { 2 } + 1 , g ( x ) = 6 x - 5$$
Find $( f g ) ( x )$.

Accepted Answer

A)  $6 x ^ { 3 } - 5 x ^ { 2 } + 6 x - 5$ 
B)  $6 x ^ { 3 } - 5$ 
C)  $6 x ^ { 3 } + 6 x ^ { 2 } - 5 x - 5$ 
D)  $6 x ^ { 2 } + 6 x - 5$ 
A)  $6 x ^ { 3 } - 5 x ^ { 2 } + 6 x - 5$ 
B)  $6 x ^ { 3 } - 5$ 
C)  $6 x ^ { 3 } + 6 x ^ { 2 } - 5 x - 5$ 
D)  $6 x ^ { 2 } + 6 x - 5$

Question 10

Describe how the graph of the equation relates to the graph $$y = x ^ { 2 }$$
-$f ( x ) = ( x - 7 ) ^ { 2 } + 9$

Accepted Answer

A)  a translation 7 units to the left and 9 units up 
B)  a translation 9 units to the right and 7 units up 
C)  a translation 7 units to the left and 9 units down 
D)  a translation 7 units to the right and 9 units up 
A)  a translation 7 units to the left and 9 units up 
B)  a translation 9 units to the right and 7 units up 
C)  a translation 7 units to the left and 9 units down 
D)  a translation 7 units to the right and 9 units up

Question 11

Select the equation that describes the graph shown.

Accepted Answer

A)  $y = - \frac { 1 } { 2 } x ^ { 2 }$ 
B)  $y = - 2 x ^ { 2 }$ 
C)  $y = - x ^ { 2 }$ 
D)  $y = 2 x ^ { 2 }$ 
A)  $y = - \frac { 1 } { 2 } x ^ { 2 }$ 
B)  $y = - 2 x ^ { 2 }$ 
C)  $y = - x ^ { 2 }$ 
D)  $y = 2 x ^ { 2 }$

Question 12

Write an equation for the line described. Give your answer in slope-intercept form.
-$$\mathrm { m } = \frac { 8 } { 3 } , \text { through } ( 4 , - 5 )$$

Accepted Answer

A)  $y = \frac { 3 } { 8 } x - \frac { 47 } { 8 }$ 
B)  $y = - \frac { 8 } { 3 } x + \frac { 47 } { 3 }$ 
C)  $y = \frac { 8 } { 3 } x - \frac { 47 } { 3 }$ 
D)  $y = \frac { 8 } { 3 } x + \frac { 47 } { 3 }$ 
A)  $y = \frac { 3 } { 8 } x - \frac { 47 } { 8 }$ 
B)  $y = - \frac { 8 } { 3 } x + \frac { 47 } { 3 }$ 
C)  $y = \frac { 8 } { 3 } x - \frac { 47 } { 3 }$ 
D)  $y = \frac { 8 } { 3 } x + \frac { 47 } { 3 }$

Question 13

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$
-$$f ( x ) = \frac { x - 10 } { x + 3 }$$

Accepted Answer

A)  $\frac { 14 } { ( x + 3 ) ( x - 3 ) }$ 
B)  $- \frac { 13 } { x ( x + 3 ) }$ 
C)  $\frac { 13 ( x + h + 3 ) } { ( x + 3 ) }$ 
D)  $\frac { 13 } { ( x + h + 3 ) ( x + 3 ) }$ 
A)  $\frac { 14 } { ( x + 3 ) ( x - 3 ) }$ 
B)  $- \frac { 13 } { x ( x + 3 ) }$ 
C)  $\frac { 13 ( x + h + 3 ) } { ( x + 3 ) }$ 
D)  $\frac { 13 } { ( x + h + 3 ) ( x + 3 ) }$

Question 14

Find the requested value.
-$f(x)=\left\{\begin{array}{ll}
5, & \text { if } x \geq 1 \
-4-x, & \text { if } x<1
\end{array}\right.$

Accepted Answer

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

Question 15

Write all linear equations in slope-intercept form.
-By reading a graph on defense spending in the country of Warpeas, you discover that in year 0 the country spent $235 million on defense and in year 8 spent $611 million. Write a linear function that relates y (in millions
Of dollars) to x.

Accepted Answer

A)  $y = - 47 x - 235$ 
B)  $y = \frac { 1 } { 5 } x + 235$ 
C)  $y = 47 x + 235$ 
D)  $y = \frac { 423 } { 4 } x + 235$ 
A)  $y = - 47 x - 235$ 
B)  $y = \frac { 1 } { 5 } x + 235$ 
C)  $y = 47 x + 235$ 
D)  $y = \frac { 423 } { 4 } x + 235$

Question 16

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.  
-At what time was the temperature 77°?

Accepted Answer

A)  12 p.m. and 3 p.m. 
B)  11 a.m. and 12 p.m. and 3 p.m. 
C)  11 a.m. and 12 p.m. 
D)  2 p.m. 
A)  12 p.m. and 3 p.m. 
B)  11 a.m. and 12 p.m. and 3 p.m. 
C)  11 a.m. and 12 p.m. 
D)  2 p.m.

Question 17

Provide an appropriate response.
-What is the midpoint of the segment joining $( c , y )$ and $( - 5 c , 7 y )$ ?

Accepted Answer

A)  $( - 3 c , 4 y )$ 
B)  $( - 2 \mathrm { c } , 4 \mathrm { y } )$ 
C)  $( - 4 c , 8 y )$ 
D)  $( 2 c , 3 y )$ 
A)  $( - 3 c , 4 y )$ 
B)  $( - 2 \mathrm { c } , 4 \mathrm { y } )$ 
C)  $( - 4 c , 8 y )$ 
D)  $( 2 c , 3 y )$

Question 18

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

Accepted Answer

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

Question 19

Find the average rate of change illustrated in the graph.
-  Usage (in minutes)

Accepted Answer

A)  $4.00 per minute 
B)  $2.00 per minute 
C)  $0.25 per minute 
D)  $0.50 per minute 
A)  $4.00 per minute 
B)  $2.00 per minute 
C)  $0.25 per minute 
D)  $0.50 per minute

Question 20

Match the description with the correct symbolic expression.
-a vertical line

Accepted Answer

A)  $6 x - 5 y = 2$ 
B)  $y = 6 x + 2$ 
C)  $x = 6$ 
D)  $f ( x ) = - 3 x + 6$ 
A)  $6 x - 5 y = 2$ 
B)  $y = 6 x + 2$ 
C)  $x = 6$ 
D)  $f ( x ) = - 3 x + 6$

Find the center-radius form of the circle described or graphed. -

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

Find the requested value. - $\text { Using the given tables, find (f } g \text { ) (2) }$ $Find the requested value. - \text { Using the given tables, find (f } g \text { ) (2) }$

Find the slope and the y-intercept of the line. - $x + 4 y = - 5$

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints $( - 2,3 )$ and $( 8 , - 5 )$

Provide an appropriate response. -If a horizontal line is drawn through the point $( 1 , - 8 )$ , where will it intersect the $y$ -axis?

Give the domain and range of the relation. - $\{ ( 3,7 ) , ( - 2 , - 9 ) , ( - 6 , - 4 ) , ( 5,0 ) \}$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x)=|x|+4$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x)=|x|+4$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = x ^ { 2 } + 1 , g ( x ) = 6 x - 5$ Find $( f g ) ( x )$ .

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = ( x - 7 ) ^ { 2 } + 9$

Select the equation that describes the graph shown.

Write an equation for the line described. Give your answer in slope-intercept form. - $\mathrm { m } = \frac { 8 } { 3 } , \text { through } ( 4 , - 5 )$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { x - 10 } { x + 3 }$

Find the requested value. - $f(x)=\left\{\begin{array}{ll}5, & \text { if } x \geq 1 \\-4-x, & \text { if } x<1\end{array}\right.$ $Find the requested value. - f(x)=\left\{\begin{array}{ll} 5, & \text { if } x \geq 1 \\ -4-x, & \text { if } x<1 \end{array}\right.$

Write all linear equations in slope-intercept form. -By reading a graph on defense spending in the country of Warpeas, you discover that in year 0 the country spent $235 million on defense and in year 8 spent $611 million. Write a linear function that relates y (in millions Of dollars) to x.

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -At what time was the temperature 77°?

Provide an appropriate response. -What is the midpoint of the segment joining $( c , y )$ and $( - 5 c , 7 y )$ ?

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

Find the average rate of change illustrated in the graph. - Usage (in minutes)

Match the description with the correct symbolic expression. -a vertical line

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

Find the center-radius form of the circle described or graphed. -

The figure below shows the graph of a functio y=f(x)y = f ( x )y=f(x) e 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).

Find the requested value. - Using the given tables, find (f g ) (2) \text { Using the given tables, find (f } g \text { ) (2) } Using the given tables, find (f g ) (2)

Find the slope and the y-intercept of the line. - x+4y=−5x + 4 y = - 5x+4y=−5

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints (−2,3)( - 2,3 )(−2,3) and (8,−5)( 8 , - 5 )(8,−5)

Provide an appropriate response. -If a horizontal line is drawn through the point (1,−8)( 1 , - 8 )(1,−8) , where will it intersect the yyy -axis?

Give the domain and range of the relation. - {(3,7),(−2,−9),(−6,−4),(5,0)}\{ ( 3,7 ) , ( - 2 , - 9 ) , ( - 6 , - 4 ) , ( 5,0 ) \}{(3,7),(−2,−9),(−6,−4),(5,0)}

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ . - f(x)=∣x∣+4f(x)=|x|+4f(x)=∣x∣+4

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=x2+1,g(x)=6x−5f ( x ) = x ^ { 2 } + 1 , g ( x ) = 6 x - 5f(x)=x2+1,g(x)=6x−5 Find (fg)(x)( f g ) ( x )(fg)(x) .

Describe how the graph of the equation relates to the graph y=x2y = x ^ { 2 }y=x2 - f(x)=(x−7)2+9f ( x ) = ( x - 7 ) ^ { 2 } + 9f(x)=(x−7)2+9

Select the equation that describes the graph shown.

Write an equation for the line described. Give your answer in slope-intercept form. - m=83, through (4,−5)\mathrm { m } = \frac { 8 } { 3 } , \text { through } ( 4 , - 5 )m=38​, through (4,−5)

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)=x−10x+3f ( x ) = \frac { x - 10 } { x + 3 }f(x)=x+3x−10​

Find the requested value. - f(x)={5, if x≥1−4−x, if x<1f(x)=\left\{\begin{array}{ll}5, & \text { if } x \geq 1 \\-4-x, & \text { if } x<1\end{array}\right.f(x)={5,−4−x,​ if x≥1 if x<1​

Write all linear equations in slope-intercept form. -By reading a graph on defense spending in the country of Warpeas, you discover that in year 0 the country spent $235 million on defense and in year 8 spent $611 million. Write a linear function that relates y (in millions Of dollars) to x.

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -At what time was the temperature 77°?

Provide an appropriate response. -What is the midpoint of the segment joining (c,y)( c , y )(c,y) and (−5c,7y)( - 5 c , 7 y )(−5c,7y) ?

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

Find the average rate of change illustrated in the graph. - Usage (in minutes)

Match the description with the correct symbolic expression. -a vertical line

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

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

Find the requested value. - $\text { Using the given tables, find (f } g \text { ) (2) }$ $Find the requested value. - \text { Using the given tables, find (f } g \text { ) (2) }$

Find the slope and the y-intercept of the line. - $x + 4 y = - 5$

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints $( - 2,3 )$ and $( 8 , - 5 )$

Provide an appropriate response. -If a horizontal line is drawn through the point $( 1 , - 8 )$ , where will it intersect the $y$ -axis?

Give the domain and range of the relation. - $\{ ( 3,7 ) , ( - 2 , - 9 ) , ( - 6 , - 4 ) , ( 5,0 ) \}$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x)=|x|+4$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x)=|x|+4$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = x ^ { 2 } + 1 , g ( x ) = 6 x - 5$ Find $( f g ) ( x )$ .

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = ( x - 7 ) ^ { 2 } + 9$

Write an equation for the line described. Give your answer in slope-intercept form. - $\mathrm { m } = \frac { 8 } { 3 } , \text { through } ( 4 , - 5 )$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { x - 10 } { x + 3 }$

Find the requested value. - $f(x)=\left\{\begin{array}{ll}5, & \text { if } x \geq 1 \\-4-x, & \text { if } x<1\end{array}\right.$ $Find the requested value. - f(x)=\left\{\begin{array}{ll} 5, & \text { if } x \geq 1 \\ -4-x, & \text { if } x<1 \end{array}\right.$

Provide an appropriate response. -What is the midpoint of the segment joining $( c , y )$ and $( - 5 c , 7 y )$ ?

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