Question 1

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = 5 - 5 x , g ( x ) = - 3 x ^ { 2 } + 5$$
Find $( f + g ) ( x )$.

Accepted Answer

A)  $- 3 x ^ { 2 } - 5 x + 10$ 
B)  $- 8 x + 10$ 
C)  $- 3 x ^ { 2 } + 5$ 
D)  $- 8 x ^ { 2 } - 5 x + 10$ 
A)  $- 3 x ^ { 2 } - 5 x + 10$ 
B)  $- 8 x + 10$ 
C)  $- 3 x ^ { 2 } + 5$ 
D)  $- 8 x ^ { 2 } - 5 x + 10$

Question 2

The graph of a linear function f is shown. Identify the slope, y-intercept, and x-intercept.
-

Accepted Answer

A)  $\frac { 1 } { 2 } ; ( 0 , - 8 ) , ( 4,0 )$ 
B)  $\frac { 1 } { 2 } ; ( 0,4 ) , ( - 8,0 )$ 
C)  $2 ; ( 0,4 ) , ( - 8,0 )$ 
D)  $2 ; ( 0 , - 8 ) , ( 4,0 )$ 
A)  $\frac { 1 } { 2 } ; ( 0 , - 8 ) , ( 4,0 )$ 
B)  $\frac { 1 } { 2 } ; ( 0,4 ) , ( - 8,0 )$ 
C)  $2 ; ( 0,4 ) , ( - 8,0 )$ 
D)  $2 ; ( 0 , - 8 ) , ( 4,0 )$

Question 3

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$\mathrm { P } ( 13 \sqrt { 3 } , \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 3 } , 4 \sqrt { 10 } )$

Accepted Answer

A)  $\left( 6 \sqrt { 6 } , - \frac { \sqrt { 30 } } { 2 } \right)$ 
B)  $\left( 7 \sqrt { 3 } , \frac { \sqrt { 10 } } { 2 } \right)$ 
C)  $\left( 6 \sqrt { 3 } , \frac { 5 \sqrt { 10 } } { 2 } \right)$ 
D)  $( 6 \sqrt { 3 } , 5 \sqrt { 10 } )$ 
A)  $\left( 6 \sqrt { 6 } , - \frac { \sqrt { 30 } } { 2 } \right)$ 
B)  $\left( 7 \sqrt { 3 } , \frac { \sqrt { 10 } } { 2 } \right)$ 
C)  $\left( 6 \sqrt { 3 } , \frac { 5 \sqrt { 10 } } { 2 } \right)$ 
D)  $( 6 \sqrt { 3 } , 5 \sqrt { 10 } )$

Question 4

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.
-$$x ^ { 2 } - y ^ { 2 } = 4$$

Accepted Answer

A)  origin only 
B)  $x$-axis, $y$-axis 
C)  $\mathrm { y }$-axis, origin 
D)  $x$-axis, $y$-axis, origin 
A)  origin only 
B)  $x$-axis, $y$-axis 
C)  $\mathrm { y }$-axis, origin 
D)  $x$-axis, $y$-axis, origin

Question 5

Graph the line described.
-$$\text { through } ( 6,4 ) ; \mathrm { m } = 0$$

Accepted Answer

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

Question 6

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 7

Give the domain and range of the relation.
-$\text { Find } f ( - 2 ) \text { if } f = \{ ( - 2,3 ) , ( 3,0 ) , ( 0,5 ) , ( 5 , - 2 ) \}$

Accepted Answer

A)  None of these 
B)  (3, 5) 
C)  5 
D)  3 
A)  None of these 
B)  (3, 5) 
C)  5 
D)  3

Question 8

Graph the line described.
-$$\text { through } ( 10,0 ) ; \mathrm { m } = - \frac { 1 } { 5 }$$

Accepted Answer

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

Question 9

The figure below shows the graph of a functio $y = f ( x )$ e this graph to
-$$\text { Sketch the graph of } y = f ( x - 3 ) \text {. }$$

Accepted Answer

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

Question 10

Use the graph to solve the problem.
-The height h in feet of a projectile thrown upward from the roof of a building after time t seconds is shown in the graph below. How high will the projectile be after 2 s?

Accepted Answer

A)  350 ft 
B)  400 ft 
C)  375 ft 
D)  425 ft 
A)  350 ft 
B)  400 ft 
C)  375 ft 
D)  425 ft

Question 11

Find the slope and the y-intercept of the line.
-$$5 x + 8 y = 31$$

Accepted Answer

A)  slope: $\frac { 3 } { 5 } ; y$-intercept: $\left( 0 , \frac { 8 } { 31 } \right)$ 
B)  slope: $\frac { 5 } { 8 } ; y$-intercept: $\left( 0 , \frac { 31 } { 8 } \right)$ 
C)  slope: $- \frac { 5 } { 8 } ; \mathrm { y }$-intercept: $\left( 0 , \frac { 31 } { 8 } \right)$ 
D)  slope: $- \frac { 3 } { 5 } ; y$-intercept: $\left( 0 , \frac { 8 } { 31 } \right)$ 
A)  slope: $\frac { 3 } { 5 } ; y$-intercept: $\left( 0 , \frac { 8 } { 31 } \right)$ 
B)  slope: $\frac { 5 } { 8 } ; y$-intercept: $\left( 0 , \frac { 31 } { 8 } \right)$ 
C)  slope: $- \frac { 5 } { 8 } ; \mathrm { y }$-intercept: $\left( 0 , \frac { 31 } { 8 } \right)$ 
D)  slope: $- \frac { 3 } { 5 } ; y$-intercept: $\left( 0 , \frac { 8 } { 31 } \right)$

Question 12

Find all points $( x , y )$ with $x = y$ that are 5 units from $( 9,2 )$.

Accepted Answer

A)  $( 5,5 )$ and $( - 6 , - 6 )$ 
B)  $( 5,5 )$ and $( 6,6 )$ 
C)  $( - 5 , - 5 )$ and $( - 6 , - 6 )$ 
D)  $( - 5 , - 5 )$ and $( 6,6 )$ 
A)  $( 5,5 )$ and $( - 6 , - 6 )$ 
B)  $( 5,5 )$ and $( 6,6 )$ 
C)  $( - 5 , - 5 )$ and $( - 6 , - 6 )$ 
D)  $( - 5 , - 5 )$ and $( 6,6 )$

Question 13

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

Accepted Answer

A)  a translation 2 units to the left 
B)  a translation 2 units up 
C)  a translation 2 units down 
D)  a translation 2 units to the right 
A)  a translation 2 units to the left 
B)  a translation 2 units up 
C)  a translation 2 units down 
D)  a translation 2 units to the right

Question 14

Find the requested value.
-$$f ( x ) = \left\{ \begin{array} { l l } 
x ^ { 2 } - 4 , & \text { if } x  1
\end{array} \right.$$

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
number for both groups. Use the graph to answer the question.  
-Estimate B(7) and G(7) and use your estimates to estimate T(7).

Accepted Answer

A)  2.5; 4.0; 6.5 
B)  2.2; 4.3; 6.5 
C)  3.5; 4.2; 7.7 
D)  2.3; 4.0; 6.3 
A)  2.5; 4.0; 6.5 
B)  2.2; 4.3; 6.5 
C)  3.5; 4.2; 7.7 
D)  2.3; 4.0; 6.3

Question 16

Decide whether the relation defines a function.
-$y = \sqrt { 7 x - 4 }$

Accepted Answer

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

Question 17

Determine whether the three points are collinear.
-$( - 5 , - 11 ) , ( 4,7 ) , ( 9,17 )$

Accepted Answer

A) True 
 B)False

Question 18

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

Accepted Answer

A)  a vertical stretching by a factor of 5 
B)  a translation 5 units to the right 
C)  a reflection across the x-axis 
D)  a translation 5 units up 
A)  a vertical stretching by a factor of 5 
B)  a translation 5 units to the right 
C)  a reflection across the x-axis 
D)  a translation 5 units up

Question 19

Find the average rate of change illustrated in the graph.
-Regrind, Inc. regrinds used typewriter platens. The variable cost to regrind each platen is $1.30. The total cost to regrind 110 platens is $500. Find the linear cost function to regrind platens. If reground platens sell for $9.60
Each, how many must be reground and sold to break even?

Accepted Answer

A)  $C ( x ) = 1.30 x + 500 ; 46$ platens 
B)  $C ( x ) = 1.30 x + 357 ; 43$ platens 
C)  $C ( x ) = 1.30 x + 500$; 61 platens 
D)  $\mathrm { C } ( \mathrm { x } ) = 1.30 \mathrm { x } + 357 ; 33$ platens 
A)  $C ( x ) = 1.30 x + 500 ; 46$ platens 
B)  $C ( x ) = 1.30 x + 357 ; 43$ platens 
C)  $C ( x ) = 1.30 x + 500$; 61 platens 
D)  $\mathrm { C } ( \mathrm { x } ) = 1.30 \mathrm { x } + 357 ; 33$ platens

Question 20

Write all linear equations in slope-intercept form.
-The amount of time t it takes a flame to go out in a closed container is a linear function of the volume of the container x. A flame in 798 mL container takes 14 seconds to go out and a flame in a 1344 mL container takes
27 seconds. Write a linear function that relates t to x.

Accepted Answer

A)  $t = \frac { 1 } { 42 } x$ 
B)  $t = \frac { 1 } { 42 } x - 5$ 
C)  $t = \frac { 41 } { 2142 } x - \frac { 65 } { 51 }$ 
D)  $t = 42 x - 5$ 
A)  $t = \frac { 1 } { 42 } x$ 
B)  $t = \frac { 1 } { 42 } x - 5$ 
C)  $t = \frac { 41 } { 2142 } x - \frac { 65 } { 51 }$ 
D)  $t = 42 x - 5$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 5 - 5 x , g ( x ) = - 3 x ^ { 2 } + 5$ Find $( f + g ) ( x )$ .

The graph of a linear function f is shown. Identify the slope, y-intercept, and x-intercept. -

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 13 \sqrt { 3 } , \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 3 } , 4 \sqrt { 10 } )$

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. - $x ^ { 2 } - y ^ { 2 } = 4$

Graph the line described. - $\text { through } ( 6,4 ) ; \mathrm { m } = 0$ $Graph the line described. - \text { through } ( 6,4 ) ; \mathrm { m } = 0$

Decide whether the relation defines a function. -

Give the domain and range of the relation. - $\text { Find } f ( - 2 ) \text { if } f = \{ ( - 2,3 ) , ( 3,0 ) , ( 0,5 ) , ( 5 , - 2 ) \}$

Graph the line described. - $\text { through } ( 10,0 ) ; \mathrm { m } = - \frac { 1 } { 5 }$ $Graph the line described. - \text { through } ( 10,0 ) ; \mathrm { m } = - \frac { 1 } { 5 }$

The figure below shows the graph of a functio $y = f ( x )$ e this graph to - $\text { Sketch the graph of } y = f ( x - 3 ) \text {. }$ $The figure below shows the graph of a functio y = f ( x ) e this graph to - \text { Sketch the graph of } y = f ( x - 3 ) \text {. }$

Use the graph to solve the problem. -The height h in feet of a projectile thrown upward from the roof of a building after time t seconds is shown in the graph below. How high will the projectile be after 2 s?

Find the slope and the y-intercept of the line. - $5 x + 8 y = 31$

Find all points $( x , y )$ with $x = y$ that are 5 units from $( 9,2 )$ .

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

Decide whether the relation defines a function. - $y = \sqrt { 7 x - 4 }$

Determine whether the three points are collinear. - $( - 5 , - 11 ) , ( 4,7 ) , ( 9,17 )$

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

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

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=5−5x,g(x)=−3x2+5f ( x ) = 5 - 5 x , g ( x ) = - 3 x ^ { 2 } + 5f(x)=5−5x,g(x)=−3x2+5 Find (f+g)(x)( f + g ) ( x )(f+g)(x) .

The graph of a linear function f is shown. Identify the slope, y-intercept, and x-intercept. -

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(133,10),Q(−3,410)\mathrm { P } ( 13 \sqrt { 3 } , \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 3 } , 4 \sqrt { 10 } )P(133​,10​),Q(−3​,410​)

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. - x2−y2=4x ^ { 2 } - y ^ { 2 } = 4x2−y2=4

Graph the line described. - through (6,4);m=0\text { through } ( 6,4 ) ; \mathrm { m } = 0 through (6,4);m=0

Decide whether the relation defines a function. -

Give the domain and range of the relation. - Find f(−2) if f={(−2,3),(3,0),(0,5),(5,−2)}\text { Find } f ( - 2 ) \text { if } f = \{ ( - 2,3 ) , ( 3,0 ) , ( 0,5 ) , ( 5 , - 2 ) \} Find f(−2) if f={(−2,3),(3,0),(0,5),(5,−2)}

Graph the line described. - through (10,0);m=−15\text { through } ( 10,0 ) ; \mathrm { m } = - \frac { 1 } { 5 } through (10,0);m=−51​

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−3). \text { Sketch the graph of } y = f ( x - 3 ) \text {. } Sketch the graph of y=f(x−3).

Use the graph to solve the problem. -The height h in feet of a projectile thrown upward from the roof of a building after time t seconds is shown in the graph below. How high will the projectile be after 2 s?

Find the slope and the y-intercept of the line. - 5x+8y=315 x + 8 y = 315x+8y=31

Find all points (x,y)( x , y )(x,y) with x=yx = yx=y that are 5 units from (9,2)( 9,2 )(9,2) .

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

Decide whether the relation defines a function. - y=7x−4y = \sqrt { 7 x - 4 }y=7x−4​

Determine whether the three points are collinear. - (−5,−11),(4,7),(9,17)( - 5 , - 11 ) , ( 4,7 ) , ( 9,17 )(−5,−11),(4,7),(9,17)

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ . - f(x)=x3+5f ( x ) = \sqrt [ 3 ] { x } + 5f(x)=3x​+5

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

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 5 - 5 x , g ( x ) = - 3 x ^ { 2 } + 5$ Find $( f + g ) ( x )$ .

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 13 \sqrt { 3 } , \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 3 } , 4 \sqrt { 10 } )$

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. - $x ^ { 2 } - y ^ { 2 } = 4$

Graph the line described. - $\text { through } ( 6,4 ) ; \mathrm { m } = 0$ $Graph the line described. - \text { through } ( 6,4 ) ; \mathrm { m } = 0$

Give the domain and range of the relation. - $\text { Find } f ( - 2 ) \text { if } f = \{ ( - 2,3 ) , ( 3,0 ) , ( 0,5 ) , ( 5 , - 2 ) \}$

Graph the line described. - $\text { through } ( 10,0 ) ; \mathrm { m } = - \frac { 1 } { 5 }$ $Graph the line described. - \text { through } ( 10,0 ) ; \mathrm { m } = - \frac { 1 } { 5 }$

The figure below shows the graph of a functio $y = f ( x )$ e this graph to - $\text { Sketch the graph of } y = f ( x - 3 ) \text {. }$ $The figure below shows the graph of a functio y = f ( x ) e this graph to - \text { Sketch the graph of } y = f ( x - 3 ) \text {. }$

Find the slope and the y-intercept of the line. - $5 x + 8 y = 31$

Find all points $( x , y )$ with $x = y$ that are 5 units from $( 9,2 )$ .

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

Decide whether the relation defines a function. - $y = \sqrt { 7 x - 4 }$

Determine whether the three points are collinear. - $( - 5 , - 11 ) , ( 4,7 ) , ( 9,17 )$

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