Question 1

Use the graph of f to draw the graph of its inverse function.
-

Accepted Answer

A)  
B)

Question 2

Write the standard form of the equation of the circle with the given center and radius.
- (0,0) ;5( 0,0 )  ; 5(0,0) ;5

Accepted Answer

A)    x2+y2=25x ^ { 2 } + y ^ { 2 } = 25x2+y2=25 
B)    x2+y2=5x ^ { 2 } + y ^ { 2 } = 5x2+y2=5 
C)    x2+y2=10x ^ { 2 } + y ^ { 2 } = 10x2+y2=10 
D)    x2−y2=5x ^ { 2 } - y ^ { 2 } = 5x2−y2=5

Question 3

Begin by graphing the standard square root function f(x)   f(x) =xf ( x )  = \sqrt { x }f(x) =x​  . Then use transformations of this graph to graph the given function.
- h(x) =x+1h ( x )  = \sqrt { x + 1 }h(x) =x+1​

Accepted Answer

A)  
B)  
C)  
D)

Question 4

Begin by graphing the standard quadratic function f(x)   f(x) =x2f ( x )  = x ^ { 2 }f(x) =x2  . Then use transformations of this graph to graph the
given function.
- h(x) =−(x+5) 2−5h ( x )  = - ( x + 5 )  ^ { 2 } - 5h(x) =−(x+5) 2−5

Accepted Answer

A)  
B)  
C)  
D)

Question 5

Determine which two functions are inverses of each other.
- f(x) =x+44g(x) =4x+4h(x) =x−44f ( x )  = \frac { x + 4 } { 4 } \quad g ( x )  = 4 x + 4 \quad h ( x )  = \frac { x - 4 } { 4 }f(x) =4x+4​g(x) =4x+4h(x) =4x−4​

Accepted Answer

A)    g(x) g ( x ) g(x)   and h(x) 
B)    f(x) f ( x ) f(x)   and  g(x) g ( x ) g(x)  
C)    f(x) f ( x ) f(x)   and  h(x) h ( x ) h(x)  
D)   None

Question 6

Identify the intervals where the function is changing as requested.
-Increasing

Accepted Answer

A)    (−2,2) ( - 2,2 ) (−2,2)  
B)    (−3,3) ( - 3,3 ) (−3,3)  
C)    (−2,∞) ( - 2 , \infty ) (−2,∞)  
D)    (−3,∞) ( - 3 , \infty ) (−3,∞)

Question 7

Does the graph represent a function that has an inverse function?
-

Accepted Answer

A)   Yes
B)   No

Question 8

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
-

Accepted Answer

A)   function
B)   not a function

Question 9

Find the domain of the composite function f∘g.
- f(x) =2x+6;g(x) =xf ( x )  = 2 x + 6 ; \quad g ( x )  = \sqrt { x }f(x) =2x+6;g(x) =x​

Accepted Answer

A)    [0,∞) [ 0 , \infty ) [0,∞)  
B)    [−3,∞) [ - 3 , \infty ) [−3,∞)  
C)    (−∞,−3]( - \infty , - 3 ](−∞,−3]  or  [0,∞) [ 0 , \infty ) [0,∞)  
D)    (−∞,∞) ( - \infty , \infty ) (−∞,∞)

Question 10

Based on the graph, find the range of y = f(x) .
-Suppose a car rental company charges  $118\$ 118$118  for the first day and  $68\$ 68$68  for each additional or partial day. Let  S(x) S ( x ) S(x)   represent the cost of renting a car for  xxx  days. Find the value of  S(5.5) S ( 5.5 ) S(5.5)  .

Accepted Answer

A)    $458\$ 458$458 
B)    $424\$ 424$424 
C)    $492\$ 492$492 
D)    $374\$ 374$374

Question 11

Use the graph of f to draw the graph of its inverse function.
-

Accepted Answer

A)  
B)

Question 12

Find an equation for the line with the given properties.
-Passing through  (2,5) ( 2,5 ) (2,5)   and parallel to the line whose equation is  y=−2x+3y = - 2 x + 3y=−2x+3 ; point-slope form

Accepted Answer

A)    y−5=−2(x−2) y - 5 = - 2 ( x - 2 ) y−5=−2(x−2)  
B)    y−2=−2(x−5) y - 2 = - 2 ( x - 5 ) y−2=−2(x−5)  
C)    y−5=x−2y - 5 = x - 2y−5=x−2 
D)    y=2xy = 2 xy=2x

Question 13

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
- f(x) =2x2,g(x) =2x2−4f(x) =2 x^{2}, g(x) =2 x^{2}-4f(x) =2x2,g(x) =2x2−4

Accepted Answer

A)   g shifts the graph of  fff  vertically down 4 units
B)    ggg  shifts the graph of  fff  vertically down 4 units
C)   g shifts the graph of f vertically up 4 units
D)   g shifts the graph of  fff  vertically up 4 units

Question 14

Determine whether the equation defines y as a function of x.
- y=−x+6y = - \sqrt { x + 6 }y=−x+6​

Accepted Answer

A)    yyy  is a function of  xxx 
B)    yyy  is not a function of  xxx

Question 15

Determine which two functions are inverses of each other.
- f(x) =xg(x) =1xh(x) =x2f ( x )  = \sqrt { x } \quad g ( x )  = \frac { 1 } { \sqrt { x } } \quad h ( x )  = x ^ { 2 }f(x) =x​g(x) =x​1​h(x) =x2

Accepted Answer

A)    f(x) f ( x ) f(x)   and  h(x) h ( x ) h(x)  
B)    f(x) f ( x ) f(x)   and  g(x) g ( x ) g(x)  
C)    g(x) g ( x ) g(x)   and  h(x) h ( x ) h(x)  
D)   None

Question 16

Find the average rate of change of the function from  x1 to x2x _ { 1 } 	ext { to } x _ { 2 }x1​ to x2​ 
- f(x) =−3x2−xf ( x )  = - 3 x ^ { 2 } - xf(x) =−3x2−x  from  x1=5x _ { 1 } = 5x1​=5  to  x2=6x _ { 2 } = 6x2​=6

Accepted Answer

A)    −34- 34−34 
B)    −2- 2−2 
C)    12\frac { 1 } { 2 }21​ 
D)    −16- \frac { 1 } { 6 }−61​

Question 17

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
-

Accepted Answer

A)   function
B)   not a function

Question 18

Determine whether the equation defines y as a function of x.
- y=x3y = x ^ { 3 }y=x3

Accepted Answer

A)    yyy  is a function of  xxx 
B)    yyy  is not a function of  xxx

Question 19

Find the domain of the composite function f∘g.
- f(x) =x+1,g(x) =8x+10f ( x )  = x + 1 , \quad g ( x )  = \frac { 8 } { x + 10 }f(x) =x+1,g(x) =x+108​

Accepted Answer

A)    (−∞,−10) ( - \infty , - 10 ) (−∞,−10)   or  (−10,∞) ( - 10 , \infty ) (−10,∞)  
B)    (−∞,−11) ( - \infty , - 11 ) (−∞,−11)   or  (−11,∞) ( - 11 , \infty ) (−11,∞)  
C)    (−∞,−10) ( - \infty , - 10 ) (−∞,−10)   or  (−10,−1) ( - 10 , - 1 ) (−10,−1)   or  (−1,∞) ( - 1 , \infty ) (−1,∞)  
D)    (−∞,∞) ( - \infty , \infty ) (−∞,∞)

Question 20

Give the domain and range of the relation.
- {(−4,−8) ,(−12,8) ,(−10,1) ,(3,−3) ,(4,9) }\{ ( - 4 , - 8 )  , ( - 12,8 )  , ( - 10,1 )  , ( 3 , - 3 )  , ( 4,9 )  \}{(−4,−8) ,(−12,8) ,(−10,1) ,(3,−3) ,(4,9) }

Accepted Answer

A)   domain  ={4,−12,3,−4,−10};= \{ 4 , - 12,3 , - 4 , - 10 \} ;={4,−12,3,−4,−10};  range  ={9,8,−3,−8,1}= \{ 9,8 , - 3 , - 8,1 \}={9,8,−3,−8,1} 
B)   domain  ={9,8,−3,−8,1};= \{ 9,8 , - 3 , - 8,1 \} ;={9,8,−3,−8,1};  range  ={4,−12,3,−4,−10}= \{ 4 , - 12,3 , - 4 , - 10 \}={4,−12,3,−4,−10} 
C)   domain  ={4,9,−12,8,3}= \{ 4,9 , - 12,8,3 \}={4,9,−12,8,3} ; range  ={−3,−4,−8,−10,1}= \{ - 3 , - 4 , - 8 , - 10,1 \}={−3,−4,−8,−10,1} 
D)   domain  ={−3,−4,−8,−10,1};= \{ - 3 , - 4 , - 8 , - 10,1 \} ;={−3,−4,−8,−10,1};  range  ={4,9,−12,8,3}= \{ 4,9 , - 12,8,3 \}={4,9,−12,8,3}

Exam 2: Functions and Graphs

Based on the graph, find the range of y = f(x) . -Suppose a car rental company charges $\$ 118$ for the first day and $\$ 68$ for each additional or partial day. Let $S ( x )$ represent the cost of renting a car for $x$ days. Find the value of $S ( 5.5 )$ .

Correct Answer
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Identify the intervals where the function is changing as requested. -Increasing $Identify the intervals where the function is changing as requested. -Increasing A) ( - 2,2 ) B) ( - 3,3 ) C) ( - 2 , \infty ) D) ( - 3 , \infty )$

Correct Answer
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Correct Answer
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Give the domain and range of the relation. - $\{ ( - 4 , - 8 ) , ( - 12,8 ) , ( - 10,1 ) , ( 3 , - 3 ) , ( 4,9 ) \}$

Correct Answer
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Determine which two functions are inverses of each other. - $f ( x ) = \sqrt { x } \quad g ( x ) = \frac { 1 } { \sqrt { x } } \quad h ( x ) = x ^ { 2 }$

Correct Answer
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Use the graph of f to draw the graph of its inverse function. -

Correct Answer
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Use the graph of f to draw the graph of its inverse function. -

Correct Answer
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Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. -

Correct Answer
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Write the standard form of the equation of the circle with the given center and radius. - $( 0,0 ) ; 5$

Correct Answer
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Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. -

Correct Answer
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Determine whether the equation defines y as a function of x. - $y = x ^ { 3 }$

Correct Answer
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Does the graph represent a function that has an inverse function? -

Correct Answer
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Find an equation for the line with the given properties. -Passing through $( 2,5 )$ and parallel to the line whose equation is $y = - 2 x + 3$ ; point-slope form

Correct Answer
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Find the average rate of change of the function from $x _ { 1 } \text { to } x _ { 2 }$ - $f ( x ) = - 3 x ^ { 2 } - x$ from $x _ { 1 } = 5$ to $x _ { 2 } = 6$

Correct Answer
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Correct Answer
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Find the domain of the composite function f∘g. - $f ( x ) = x + 1 , \quad g ( x ) = \frac { 8 } { x + 10 }$

Correct Answer
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Correct Answer
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Determine which two functions are inverses of each other. - $f ( x ) = \frac { x + 4 } { 4 } \quad g ( x ) = 4 x + 4 \quad h ( x ) = \frac { x - 4 } { 4 }$

Correct Answer
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Determine whether the equation defines y as a function of x. - $y = - \sqrt { x + 6 }$

Correct Answer
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Find the domain of the composite function f∘g. - $f ( x ) = 2 x + 6 ; \quad g ( x ) = \sqrt { x }$

Correct Answer
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Exam 2: Functions and Graphs

Based on the graph, find the range of y = f(x) . -Suppose a car rental company charges $118\$ 118$118 for the first day and $68\$ 68$68 for each additional or partial day. Let S(x) S ( x ) S(x) represent the cost of renting a car for xxx days. Find the value of S(5.5) S ( 5.5 ) S(5.5) .

Correct AnswerverifiedShow Answer

Identify the intervals where the function is changing as requested. -Increasing

Correct AnswerverifiedShow Answer

Begin by graphing the standard square root function f(x) f(x) =xf ( x ) = \sqrt { x }f(x) =x​ . Then use transformations of this graph to graph the given function. - h(x) =x+1h ( x ) = \sqrt { x + 1 }h(x) =x+1​

Correct AnswerverifiedShow Answer

Give the domain and range of the relation. - {(−4,−8) ,(−12,8) ,(−10,1) ,(3,−3) ,(4,9) }\{ ( - 4 , - 8 ) , ( - 12,8 ) , ( - 10,1 ) , ( 3 , - 3 ) , ( 4,9 ) \}{(−4,−8) ,(−12,8) ,(−10,1) ,(3,−3) ,(4,9) }

Correct AnswerverifiedShow Answer

Determine which two functions are inverses of each other. - f(x) =xg(x) =1xh(x) =x2f ( x ) = \sqrt { x } \quad g ( x ) = \frac { 1 } { \sqrt { x } } \quad h ( x ) = x ^ { 2 }f(x) =x​g(x) =x​1​h(x) =x2

Correct AnswerverifiedShow Answer

Use the graph of f to draw the graph of its inverse function. -

Correct AnswerverifiedShow Answer

Use the graph of f to draw the graph of its inverse function. -

Correct AnswerverifiedShow Answer

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. -

Correct AnswerverifiedShow Answer

Write the standard form of the equation of the circle with the given center and radius. - (0,0) ;5( 0,0 ) ; 5(0,0) ;5

Correct AnswerverifiedShow Answer

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. -

Correct AnswerverifiedShow Answer

Determine whether the equation defines y as a function of x. - y=x3y = x ^ { 3 }y=x3

Correct AnswerverifiedShow Answer

Does the graph represent a function that has an inverse function? -

Correct AnswerverifiedShow Answer

Find an equation for the line with the given properties. -Passing through (2,5) ( 2,5 ) (2,5) and parallel to the line whose equation is y=−2x+3y = - 2 x + 3y=−2x+3 ; point-slope form

Correct AnswerverifiedShow Answer

Find the average rate of change of the function from x1 to x2x _ { 1 } \text { to } x _ { 2 }x1​ to x2​ - f(x) =−3x2−xf ( x ) = - 3 x ^ { 2 } - xf(x) =−3x2−x from x1=5x _ { 1 } = 5x1​=5 to x2=6x _ { 2 } = 6x2​=6

Correct AnswerverifiedShow Answer

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph of f. - f(x) =2x2,g(x) =2x2−4f(x) =2 x^{2}, g(x) =2 x^{2}-4f(x) =2x2,g(x) =2x2−4

Correct AnswerverifiedShow Answer

Find the domain of the composite function f∘g. - f(x) =x+1,g(x) =8x+10f ( x ) = x + 1 , \quad g ( x ) = \frac { 8 } { x + 10 }f(x) =x+1,g(x) =x+108​

Correct AnswerverifiedShow Answer

Begin by graphing the standard quadratic function f(x) f(x) =x2f ( x ) = x ^ { 2 }f(x) =x2 . Then use transformations of this graph to graph the given function. - h(x) =−(x+5) 2−5h ( x ) = - ( x + 5 ) ^ { 2 } - 5h(x) =−(x+5) 2−5

Correct AnswerverifiedShow Answer

Determine which two functions are inverses of each other. - f(x) =x+44g(x) =4x+4h(x) =x−44f ( x ) = \frac { x + 4 } { 4 } \quad g ( x ) = 4 x + 4 \quad h ( x ) = \frac { x - 4 } { 4 }f(x) =4x+4​g(x) =4x+4h(x) =4x−4​

Correct AnswerverifiedShow Answer

Determine whether the equation defines y as a function of x. - y=−x+6y = - \sqrt { x + 6 }y=−x+6​

Correct AnswerverifiedShow Answer

Find the domain of the composite function f∘g. - f(x) =2x+6;g(x) =xf ( x ) = 2 x + 6 ; \quad g ( x ) = \sqrt { x }f(x) =2x+6;g(x) =x​

Correct AnswerverifiedShow Answer

Based on the graph, find the range of y = f(x) . -Suppose a car rental company charges $\$ 118$ for the first day and $\$ 68$ for each additional or partial day. Let $S ( x )$ represent the cost of renting a car for $x$ days. Find the value of $S ( 5.5 )$ .

Correct Answer
verified

Identify the intervals where the function is changing as requested. -Increasing $Identify the intervals where the function is changing as requested. -Increasing A) ( - 2,2 ) B) ( - 3,3 ) C) ( - 2 , \infty ) D) ( - 3 , \infty )$

Correct Answer
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Correct Answer
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Give the domain and range of the relation. - $\{ ( - 4 , - 8 ) , ( - 12,8 ) , ( - 10,1 ) , ( 3 , - 3 ) , ( 4,9 ) \}$

Correct Answer
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Determine which two functions are inverses of each other. - $f ( x ) = \sqrt { x } \quad g ( x ) = \frac { 1 } { \sqrt { x } } \quad h ( x ) = x ^ { 2 }$

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Write the standard form of the equation of the circle with the given center and radius. - $( 0,0 ) ; 5$

Correct Answer
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Correct Answer
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Determine whether the equation defines y as a function of x. - $y = x ^ { 3 }$

Correct Answer
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Correct Answer
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Find an equation for the line with the given properties. -Passing through $( 2,5 )$ and parallel to the line whose equation is $y = - 2 x + 3$ ; point-slope form

Correct Answer
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Find the average rate of change of the function from $x _ { 1 } \text { to } x _ { 2 }$ - $f ( x ) = - 3 x ^ { 2 } - x$ from $x _ { 1 } = 5$ to $x _ { 2 } = 6$

Correct Answer
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Correct Answer
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Find the domain of the composite function f∘g. - $f ( x ) = x + 1 , \quad g ( x ) = \frac { 8 } { x + 10 }$

Correct Answer
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Correct Answer
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Determine which two functions are inverses of each other. - $f ( x ) = \frac { x + 4 } { 4 } \quad g ( x ) = 4 x + 4 \quad h ( x ) = \frac { x - 4 } { 4 }$

Correct Answer
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Determine whether the equation defines y as a function of x. - $y = - \sqrt { x + 6 }$

Correct Answer
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Find the domain of the composite function f∘g. - $f ( x ) = 2 x + 6 ; \quad g ( x ) = \sqrt { x }$

Correct Answer
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