Question 1

Describe how the graph of the equation relates to the graph of y  y=x3y = \sqrt [ 3 ] { x }y=3x​  .
- y=∣x−7∣−5y=|x-7|-5y=∣x−7∣−5

Accepted Answer

A)  
B)  
C)  
D)

Question 2

For the given functions f and g , find the indicated composition.
- f(x) =4x2+2x+7,g(x) =2x−8f ( x )  = 4 x ^ { 2 } + 2 x + 7 , \quad g ( x )  = 2 x - 8f(x) =4x2+2x+7,g(x) =2x−8 
 (gf) (x) ( g f )  ( x ) (gf) (x)

Accepted Answer

A)    4x2+2x−14 x ^ { 2 } + 2 x - 14x2+2x−1 
B)    8x2+4x+68 x ^ { 2 } + 4 x + 68x2+4x+6 
C)    4x2+4x+64 x ^ { 2 } + 4 x + 64x2+4x+6 
D)    8x2+4x+228 x ^ { 2 } + 4 x + 228x2+4x+22

Question 3

Graph the point symmetric to the given point.
-Plot the point (2, 0) , then plot the point that is symmetric to (2, 0)  with respect to the y-axis.

Accepted Answer

A)  
B)  
C)  
D)

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.
- y=2x4+8x−4y = 2 x ^ { 4 } + 8 x - 4y=2x4+8x−4

Accepted Answer

A)    yyy -axis only
B)   origin only
C)   x-axis only
D)   none of these

Question 5

Find the requested function value.
-Find  (f∘g) (3) ( f \circ g )  ( 3 ) (f∘g) (3)   when  f(x) =−8x+5f ( x )  = - 8 x + 5f(x) =−8x+5  and  g(x) =−3x2−7x+5g ( x )  = - 3 x ^ { 2 } - 7 x + 5g(x) =−3x2−7x+5 .

Accepted Answer

A)   195
B)   349
C)    −945- 945−945 
D)   205

Question 6

Find the specified domain.
-Find the domain of  (f−g) (x) ( f - g )  ( x ) (f−g) (x)   when  f(x) =8x−2f ( x )  = 8 x - 2f(x) =8x−2  and  g(x) =5x−4g ( x )  = 5 x - 4g(x) =5x−4 .

Accepted Answer

A)    (−8,2) ( - 8,2 ) (−8,2)  
B)    (−8,∞) ( - 8 , \infty ) (−8,∞)  
C)    (−2,8) ( - 2,8 ) (−2,8)  
D)    (−∞,∞) ( - \infty , \infty ) (−∞,∞)

Question 7

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x) .
- 14x+4y=414 x + 4 y = 414x+4y=4

Accepted Answer

A)    f(x) =72x+1f ( x )  = \frac { 7 } { 2 } x + 1f(x) =27​x+1 
B)    f(x) =72x−1f ( x )  = \frac { 7 } { 2 } x - 1f(x) =27​x−1 
C)    f(x) =14x−4f ( x )  = 14 x - 4f(x) =14x−4 
D)    f(x) =−72x+1f ( x )  = - \frac { 7 } { 2 } x + 1f(x) =−27​x+1

Question 8

Decide whether the relation defines a function.
- y=x3y = x ^ { 3 }y=x3

Accepted Answer

A)   Not a function
B)   Function

Question 9

Decide whether the relation defines a function.
- {(−5,4) ,(−2,−8) ,(−1,8) ,(7,−2) }\{ ( - 5,4 )  , ( - 2 , - 8 )  , ( - 1,8 )  , ( 7 , - 2 )  \}{(−5,4) ,(−2,−8) ,(−1,8) ,(7,−2) }

Accepted Answer

A)   Not a function
B)   Function

Question 10

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. 
-The volume of water added to a circular drum of radius r is given by V  Vw=25t, where Vw\mathrm { V } _ { \mathrm { w } } = 25 \mathrm { t } , 	ext { where } \mathrm { V } _ { \mathrm { w } }Vw​=25t, where Vw​  is volume in cu ft and t is time in sec. Find the depth of water in a drum of radius 6 ft after adding water for 18 sec. (Round result to
One decimal place.)

Accepted Answer

A)   8.0 ft
B)   2.0 ft
C)   12.6 ft
D)   4.0 ft

Question 11

Select the equation that describes the graph shown.

Accepted Answer

A)    y=(x−2) 2+2y = ( x - 2 )  ^ { 2 } + 2y=(x−2) 2+2 
B)    y=x2−2y = x ^ { 2 } - 2y=x2−2 
C)    y=(x+2) 2y = ( x + 2 )  ^ { 2 }y=(x+2) 2 
D)    y=(x−2) 2y = ( x - 2 )  ^ { 2 }y=(x−2) 2

Question 12

Find the specified domain.
-Find the domain of  (fg) (x) \left( \frac { f } { g } \right)  ( x ) (gf​) (x)   when  f(x) =2x−6f ( x )  = 2 x - 6f(x) =2x−6  and  g(x) =7x−2g ( x )  = 7 x - 2g(x) =7x−2

Accepted Answer

A)    (∞,27) ∪(27,∞) \left( \infty , \frac { 2 } { 7 } \right)  \cup \left( \frac { 2 } { 7 } , \infty \right) (∞,72​) ∪(72​,∞)  
B)    (−∞,3) ∪(3,∞) ( - \infty , 3 )  \cup ( 3 , \infty ) (−∞,3) ∪(3,∞)  
C)    (−∞,∞) ( - \infty , \infty ) (−∞,∞)  
D)    (∞,27) ∪(27,3) ∪(3,∞) \left( \infty , \frac { 2 } { 7 } \right)  \cup \left( \frac { 2 } { 7 } , 3 \right)  \cup ( 3 , \infty ) (∞,72​) ∪(72​,3) ∪(3,∞)

Question 13

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

Accepted Answer

A)  
B)  
C)  
D)

Question 14

Graph the equation by plotting points.
- y=x−4y=\sqrt{x}-4y=x​−4

Accepted Answer

A)  
B)  
C)  
D)

Question 15

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope-intercept form.
-

Accepted Answer

A)    y=x−1y = x - 1y=x−1 
B)    y=−x+1y = - x + 1y=−x+1 
C)    y=x+1y = x + 1y=x+1 
D)    y=−x−1y = - x - 1y=−x−1

Question 16

Graph the equation by plotting points.
- y=x−3y=\sqrt{x-3}y=x−3​

Accepted Answer

A)  
B)  
C)  
D)

Question 17

Write all linear equations in slope-intercept form.
-A biologist recorded 6 snakes on 16 acres in one area and 15 snakes on 33 acres in another area. Find a linear equation that models the number of snakes in x acres.

Accepted Answer

A)    y=x+10y = x + 10y=x+10 
B)    y=917x+4217y = \frac { 9 } { 17 } x + \frac { 42 } { 17 }y=179​x+1742​ 
C)    y=917x−4217y = \frac { 9 } { 17 } x - \frac { 42 } { 17 }y=179​x−1742​ 
D)    y=179x−1742y = \frac { 17 } { 9 } x - \frac { 17 } { 42 }y=917​x−4217​

Question 18

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
- x2+y2+10x−18y+42=0x ^ { 2 } + y ^ { 2 } + 10 x - 18 y + 42 = 0x2+y2+10x−18y+42=0

Accepted Answer

A)   no; the graph is the point  (5,−9) ( 5 , - 9 ) (5,−9)  
B)   yes
C)   no; the graph is nonexistent
D)   no; the graph is the point  (−5,9) ( - 5,9 ) (−5,9)

Question 19

Describe how the graph of the equation relates to the graph of y  y=x3y = \sqrt [ 3 ] { x }y=3x​  .
- f(x) =14x3f(x) =\frac{1}{4} x^{3}f(x) =41​x3

Accepted Answer

A)  
B)  
C)  
D)

Question 20

Use a graphing calculator to solve the linear equation.
-The graph of  y1\mathrm { y } _ { 1 }y1​  is shown in the standard viewing window. Which is the only choice that could possibly be the solution of the equation  y1=0\mathrm { y } _ { 1 } = 0y1​=0  ?

−12,−7,−134,12- 12 , - 7 , - \frac { 13 } { 4 } , 12−12,−7,−413​,12

Accepted Answer

A)    −7- 7−7 
B)    −12- 12−12 
C)   12
D)    −134- \frac { 13 } { 4 }−413​

Exam 3: Graphs and Functions

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } + 10 x - 18 y + 42 = 0$

Correct Answer
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Graph the point symmetric to the given point. -Plot the point (2, 0) , then plot the point that is symmetric to (2, 0) with respect to the y-axis.

Correct Answer
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For the given functions f and g , find the indicated composition. - $f ( x ) = 4 x ^ { 2 } + 2 x + 7 , \quad g ( x ) = 2 x - 8$ $( g f ) ( x )$

Correct Answer
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Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x) =|5 x|$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x) =|5 x| A) B) C) D)$

Correct Answer
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Correct Answer
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Graph the equation by plotting points. - $y=\sqrt{x-3}$ $Graph the equation by plotting points. - y=\sqrt{x-3} A) B) C) D)$

Correct Answer
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Decide whether the relation defines a function. - $y = x ^ { 3 }$

Correct Answer
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Graph the equation by plotting points. - $y=\sqrt{x}-4$ $Graph the equation by plotting points. - y=\sqrt{x}-4 A) B) C) D)$

Correct Answer
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The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope-intercept form. -

Correct Answer
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Correct Answer
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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. - $y = 2 x ^ { 4 } + 8 x - 4$

Correct Answer
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Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x) =\frac{1}{4} x^{3}$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x) =\frac{1}{4} x^{3} A) B) C) D)$

Correct Answer
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Find the specified domain. -Find the domain of $( f - g ) ( x )$ when $f ( x ) = 8 x - 2$ and $g ( x ) = 5 x - 4$ .

Correct Answer
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Write all linear equations in slope-intercept form. -A biologist recorded 6 snakes on 16 acres in one area and 15 snakes on 33 acres in another area. Find a linear equation that models the number of snakes in x acres.

Correct Answer
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Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $y=|x-7|-5$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - y=|x-7|-5 A) B) C) D)$

Correct Answer
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Select the equation that describes the graph shown. $Select the equation that describes the graph shown. A) y = ( x - 2 ) ^ { 2 } + 2 B) y = x ^ { 2 } - 2 C) y = ( x + 2 ) ^ { 2 } D) y = ( x - 2 ) ^ { 2 }$

Correct Answer
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Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = 2 x - 6$ and $g ( x ) = 7 x - 2$

Correct Answer
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Find the requested function value. -Find $( f \circ g ) ( 3 )$ when $f ( x ) = - 8 x + 5$ and $g ( x ) = - 3 x ^ { 2 } - 7 x + 5$ .

Correct Answer
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Decide whether the relation defines a function. - $\{ ( - 5,4 ) , ( - 2 , - 8 ) , ( - 1,8 ) , ( 7 , - 2 ) \}$

Correct Answer
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An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x) . - $14 x + 4 y = 4$

Correct Answer
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Exam 3: Graphs and Functions

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - x2+y2+10x−18y+42=0x ^ { 2 } + y ^ { 2 } + 10 x - 18 y + 42 = 0x2+y2+10x−18y+42=0

Correct AnswerverifiedShow Answer

Graph the point symmetric to the given point. -Plot the point (2, 0) , then plot the point that is symmetric to (2, 0) with respect to the y-axis.

Correct AnswerverifiedShow Answer

For the given functions f and g , find the indicated composition. - f(x) =4x2+2x+7,g(x) =2x−8f ( x ) = 4 x ^ { 2 } + 2 x + 7 , \quad g ( x ) = 2 x - 8f(x) =4x2+2x+7,g(x) =2x−8 (gf) (x) ( g f ) ( x ) (gf) (x)

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Graph the equation by plotting points. - y=x−3y=\sqrt{x-3}y=x−3​

Correct AnswerverifiedShow Answer

Decide whether the relation defines a function. - y=x3y = x ^ { 3 }y=x3

Correct AnswerverifiedShow Answer

Graph the equation by plotting points. - y=x−4y=\sqrt{x}-4y=x​−4

Correct AnswerverifiedShow Answer

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope-intercept form. -

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

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. - y=2x4+8x−4y = 2 x ^ { 4 } + 8 x - 4y=2x4+8x−4

Correct AnswerverifiedShow Answer

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ . - f(x) =14x3f(x) =\frac{1}{4} x^{3}f(x) =41​x3

Correct AnswerverifiedShow Answer

Find the specified domain. -Find the domain of (f−g) (x) ( f - g ) ( x ) (f−g) (x) when f(x) =8x−2f ( x ) = 8 x - 2f(x) =8x−2 and g(x) =5x−4g ( x ) = 5 x - 4g(x) =5x−4 .

Correct AnswerverifiedShow Answer

Write all linear equations in slope-intercept form. -A biologist recorded 6 snakes on 16 acres in one area and 15 snakes on 33 acres in another area. Find a linear equation that models the number of snakes in x acres.

Correct AnswerverifiedShow Answer

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ . - y=∣x−7∣−5y=|x-7|-5y=∣x−7∣−5

Correct AnswerverifiedShow Answer

Select the equation that describes the graph shown.

Correct AnswerverifiedShow Answer

Find the specified domain. -Find the domain of (fg) (x) \left( \frac { f } { g } \right) ( x ) (gf​) (x) when f(x) =2x−6f ( x ) = 2 x - 6f(x) =2x−6 and g(x) =7x−2g ( x ) = 7 x - 2g(x) =7x−2

Correct AnswerverifiedShow Answer

Find the requested function value. -Find (f∘g) (3) ( f \circ g ) ( 3 ) (f∘g) (3) when f(x) =−8x+5f ( x ) = - 8 x + 5f(x) =−8x+5 and g(x) =−3x2−7x+5g ( x ) = - 3 x ^ { 2 } - 7 x + 5g(x) =−3x2−7x+5 .

Correct AnswerverifiedShow Answer

Decide whether the relation defines a function. - {(−5,4) ,(−2,−8) ,(−1,8) ,(7,−2) }\{ ( - 5,4 ) , ( - 2 , - 8 ) , ( - 1,8 ) , ( 7 , - 2 ) \}{(−5,4) ,(−2,−8) ,(−1,8) ,(7,−2) }

Correct AnswerverifiedShow Answer

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x) . - 14x+4y=414 x + 4 y = 414x+4y=4

Correct AnswerverifiedShow Answer

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } + 10 x - 18 y + 42 = 0$

Correct Answer
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Correct Answer
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For the given functions f and g , find the indicated composition. - $f ( x ) = 4 x ^ { 2 } + 2 x + 7 , \quad g ( x ) = 2 x - 8$ $( g f ) ( x )$

Correct Answer
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Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x) =|5 x|$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x) =|5 x| A) B) C) D)$

Correct Answer
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Correct Answer
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Graph the equation by plotting points. - $y=\sqrt{x-3}$ $Graph the equation by plotting points. - y=\sqrt{x-3} A) B) C) D)$

Correct Answer
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Decide whether the relation defines a function. - $y = x ^ { 3 }$

Correct Answer
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Graph the equation by plotting points. - $y=\sqrt{x}-4$ $Graph the equation by plotting points. - y=\sqrt{x}-4 A) B) C) D)$

Correct Answer
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Correct Answer
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Correct Answer
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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. - $y = 2 x ^ { 4 } + 8 x - 4$

Correct Answer
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Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x) =\frac{1}{4} x^{3}$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x) =\frac{1}{4} x^{3} A) B) C) D)$

Correct Answer
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Find the specified domain. -Find the domain of $( f - g ) ( x )$ when $f ( x ) = 8 x - 2$ and $g ( x ) = 5 x - 4$ .

Correct Answer
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Correct Answer
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Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $y=|x-7|-5$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - y=|x-7|-5 A) B) C) D)$

Correct Answer
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Select the equation that describes the graph shown. $Select the equation that describes the graph shown. A) y = ( x - 2 ) ^ { 2 } + 2 B) y = x ^ { 2 } - 2 C) y = ( x + 2 ) ^ { 2 } D) y = ( x - 2 ) ^ { 2 }$

Correct Answer
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Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = 2 x - 6$ and $g ( x ) = 7 x - 2$

Correct Answer
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Find the requested function value. -Find $( f \circ g ) ( 3 )$ when $f ( x ) = - 8 x + 5$ and $g ( x ) = - 3 x ^ { 2 } - 7 x + 5$ .

Correct Answer
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Decide whether the relation defines a function. - $\{ ( - 5,4 ) , ( - 2 , - 8 ) , ( - 1,8 ) , ( 7 , - 2 ) \}$

Correct Answer
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An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x) . - $14 x + 4 y = 4$

Correct Answer
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