Question 1

Graph the function.
-f(x) = -2

Accepted Answer

A)  
B)   
C)  
D)  E) A) and B)
F) B) and C)

Question 2

Use the vertical line test to determine whether the graph represents a function.
-

Accepted Answer

A)  function
B)  not a functionC) A) and B)
D) undefined

Question 3

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.
-Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?

Accepted Answer

A)  f has a relative maximum at x = 0; the relative maximum is 1
B)  f has a relative maximum at x = -3 and 3; the relative maximum is 0
C)  f has no relative maximum
D)  f has a relative maximum at x = 3; the relative maximum is 1E) B) and C)
F) A) and B)

Question 4

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
- f(x) =4x+5;g(x) =6x−1;f ( x )  = 4 x + 5 ; g ( x )  = 6 x - 1 ; \quadf(x) =4x+5;g(x) =6x−1;  Find  fg\frac { f } { g }gf​

Accepted Answer

A)    (fg) (x) =4x+56x−1;(∞,16) ∪(16,∞) \left( \frac { \mathrm { f } } { \mathrm { g } } \right)  ( \mathrm { x } )  = \frac { 4 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left( \infty , \frac { 1 } { 6 } \right)  \cup \left( \frac { 1 } { 6 } , \infty \right) (gf​) (x) =6x−14x+5​;(∞,61​) ∪(61​,∞)  
B)    (fg) (x) =6x−14x+5;(∞,16) ∪(16,∞) \left( \frac { f } { g } \right)  ( x )  = \frac { 6 x - 1 } { 4 x + 5 } ; \left( \infty , \frac { 1 } { 6 } \right)  \cup \left( \frac { 1 } { 6 } , \infty \right) (gf​) (x) =4x+56x−1​;(∞,61​) ∪(61​,∞)  
C)    (fg) (x) =6x−14x+5;(∞,−54) ∪(−54,∞) \left( \frac { f } { g } \right)  ( x )  = \frac { 6 x - 1 } { 4 x + 5 } ; \left( \infty , - \frac { 5 } { 4 } \right)  \cup \left( - \frac { 5 } { 4 } , \infty \right) (gf​) (x) =4x+56x−1​;(∞,−45​) ∪(−45​,∞)  
D)    (fg) (x) =4x+56x−1;(∞,−54) ∪(−54,∞) \left( \frac { \mathrm { f } } { \mathrm { g } } \right)  ( \mathrm { x } )  = \frac { 4 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left( \infty , - \frac { 5 } { 4 } \right)  \cup \left( - \frac { 5 } { 4 } , \infty \right) (gf​) (x) =6x−14x+5​;(∞,−45​) ∪(−45​,∞) E) A) and B)
F) A) and C)

Question 5

Use the horizontal line test to determine whether the function is one-to-one.
-

Accepted Answer

A)  Yes
B)  NoC) A) and B)
D) undefined

Question 6

Find the x-intercept(s) and the y-intercept of the function.
-f(x) = -2

Accepted Answer

A)  (-2, 0) , no y-intercept
B)  no x-intercept, (0, -2) 
C)  no x-intercept, no y-intercept
D)  (-2, 0) , (0, -2) E) B) and C)
F) A) and D)

Question 7

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
-

Accepted Answer

A)   domain:  [0,4][ 0,4 ][0,4] range:  (−∞,∞) ( - \infty , \infty ) (−∞,∞)  
B)   domain:  (−∞,∞) ( - \infty , \infty ) (−∞,∞)  range:  [0,4][ 0,4 ][0,4] 
C)   domain:  (−∞,∞) ( - \infty , \infty ) (−∞,∞)  range:  [3,4][ 3,4 ][3,4] 
D)   domain:  [3,4][ 3,4 ][3,4] range:  (−∞,∞) ( - \infty , \infty ) (−∞,∞) E) A) and B)
F) A) and C)

Question 8

Find the domain of the composite function f g. Write the domain in interval notation.
- f(x) =8x+56,g(x) =x+6f ( x )  = 8 x + 56 , g ( x )  = x + 6f(x) =8x+56,g(x) =x+6

Accepted Answer

A)    (−∞,∞) ( - \infty , \infty ) (−∞,∞)  
B)    (−∞,−7) ∪(−7,−6) (−6,∞) ( - \infty , - 7 )  \cup ( - 7 , - 6 )  ( - 6 , \infty ) (−∞,−7) ∪(−7,−6) (−6,∞)  
C)    (−∞,−13) ∪(−13,∞) ( - \infty , - 13 )  \cup ( - 13 , \infty ) (−∞,−13) ∪(−13,∞)  
D)    (−∞,13) ∪(13,∞) ( - \infty , 13 )  \cup ( 13 , \infty ) (−∞,13) ∪(13,∞) E) B) and D)
F) B) and C)

Question 9

Use the vertical line test to determine whether the graph represents a function.
-

Accepted Answer

A)  function
B)  not a functionC) A) and B)
D) undefined

Question 10

Use the accompanying graph of y = f(x)  to sketch the graph of the indicated equation.
- y=2f(x) y=2 f(x) y=2f(x)

Accepted Answer

A)  
B)  
C)  
D)   E) All of the above
F) A) and B)

Question 11

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
- f(x) =1x+3f ( x )  = \frac { 1 } { x + 3 }f(x) =x+31​

Accepted Answer

A)  
B)  
C)  
D)   E) C) and D)
F) B) and D)

Question 12

Decide whether or not the functions are inverses of each other.
- f(x) =x+3,x≥−3;g(x) =x2+3f ( x )  = \sqrt { x + 3 } , x \geq - 3 ; g ( x )  = x ^ { 2 } + 3f(x) =x+3​,x≥−3;g(x) =x2+3

Accepted Answer

A)  Yes
B)  No C) A) and B)
D) undefined

Question 13

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
- f(x) =x−3−6f(x) =\sqrt{x-3}-6f(x) =x−3​−6

Accepted Answer

A)  
B)  
C)  
D)   E) None of the above
F) A) and B)

Question 14

The graph of a function f is given. Use the graph to answer the question.
-Find the values of x, if any, at which f has a relative minimum. What are the relative minima?

Accepted Answer

A)  f has a relative minimum at x = 0; the relative minimum is 2
B)  f has no relative minimum
C)  f has a relative minimum at x = -2 and 2; the relative minimum is 0
D)  f has a relative minimum at x = -2; the relative minimum is 0E) None of the above
F) B) and D)

Question 15

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
- f(x) =−∣x∣f(x) =-|x|f(x) =−∣x∣

Accepted Answer

A)  
B)  
C)  
D)   E) B) and D)
F) All of the above

Question 16

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.
-(- 1, 0)

Accepted Answer

A)  constant
B)  decreasing
C)  increasingD) A) and C)
E) All of the above

Question 17

Find the rule that defines each piecewise-defined function.
- 0 \end{array} ight.  C)   f ( x )  = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & 	ext { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & 	ext { if } x \geq 0 \end{array} ight.  D)   f ( x )  = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x + 4 & 	ext { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & 	ext { if } x > 0 \end{array} ight." class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

A) f(x) ={43x+4 if −3≤x≤023x if 0f(x) ={34x+4 if −3≤x≤032x if x>0f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & ext { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & ext { if } x > 0 \end{array} ight.f(x) ={43x+423x if −3≤x≤0 if x>0 C) f(x) ={34x+4 if −3≤x≤032x if x≥0f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & ext { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & ext { if } x \geq 0 \end{array} ight.f(x) ={43x+423x if −3≤x≤0 if x≥0 D) 0 \end{array} ight.">f(x) ={43x+4 if −3≤x≤023x if x>0f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x + 4 & ext { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & ext { if } x > 0 \end{array} ight.f(x) ={34x+432x if −3≤x≤0 if x>0E) C) and D) F) A) and B)

Question 18

Solve the problem.
-A cellular phone plan had the following schedule of charges: 
 What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls.

Accepted Answer

$27.50 $32.50;   \[C ( x ) = \left\{ \begi ...

Question 19

For the given functions f and g, find the requested composite function.
- f(x) =x+7,g(x) =8x−11;f ( x )  = \sqrt { x + 7 } , g ( x )  = 8 x - 11 ; \quadf(x) =x+7​,g(x) =8x−11;  Find the function  f∘gf \circ gf∘g .

Accepted Answer

A)    8x+7−118 \sqrt { x + 7 } - 118x+7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​−11 
B)    22x−12 \sqrt { 2 x - 1 }22x−1c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    8x−48 \sqrt { x - 4 }8x−4c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    22x+12 \sqrt { 2 x + 1 }22x+1c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​E) A) and B)
F) All of the above

Question 20

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
- f(x) =∣x−3∣+2f ( x )  = | x - 3 | + 2f(x) =∣x−3∣+2

Accepted Answer

A)  
B)  
C)  
D)   E) A) and D)
F) A) and C)

Exam 3: Functions

The graph of a function f is given. Use the graph to answer the question. -Find the values of x, if any, at which f has a relative minimum. What are the relative minima?

Correct Answer
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Correct Answer
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For the given functions f and g, find the requested composite function. - $f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quad$ Find the function $f \circ g$ .

Correct Answer
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For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quad$ Find $\frac { f } { g }$

Correct Answer
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Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = | x - 3 | + 2$

Correct Answer
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Correct Answer
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Use the vertical line test to determine whether the graph represents a function. -

Correct Answer
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Find the x-intercept(s) and the y-intercept of the function. -f(x) = -2

Correct Answer
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Use the horizontal line test to determine whether the function is one-to-one. -

Correct Answer
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Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3$

Correct Answer
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Use the vertical line test to determine whether the graph represents a function. -

Correct Answer
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The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(- 1, 0)

Correct Answer
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The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?

Correct Answer
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Solve the problem. -A cellular phone plan had the following schedule of charges: What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls.

Correct Answer
verified
$27.50 $32.50; \[C ( x ) = \left\{ \begi ...
View Answer

Find the domain of the composite function f g. Write the domain in interval notation. - $f ( x ) = 8 x + 56 , g ( x ) = x + 6$

Correct Answer
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Graph the function. -f(x) = -2

Correct Answer
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Correct Answer
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Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x) =-|x|$

Correct Answer
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Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - $y=2 f(x)$

Correct Answer
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Exam 3: Functions

The graph of a function f is given. Use the graph to answer the question. -Find the values of x, if any, at which f has a relative minimum. What are the relative minima?

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Find the rule that defines each piecewise-defined function. -

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For the given functions f and g, find the requested composite function. - f(x) =x+7,g(x) =8x−11;f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quadf(x) =x+7​,g(x) =8x−11; Find the function f∘gf \circ gf∘g .

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For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - f(x) =4x+5;g(x) =6x−1;f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quadf(x) =4x+5;g(x) =6x−1; Find fg\frac { f } { g }gf​

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Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x) =∣x−3∣+2f ( x ) = | x - 3 | + 2f(x) =∣x−3∣+2

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Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x) =x−3−6f(x) =\sqrt{x-3}-6f(x) =x−3​−6

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Use the vertical line test to determine whether the graph represents a function. -

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Find the x-intercept(s) and the y-intercept of the function. -f(x) = -2

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Use the horizontal line test to determine whether the function is one-to-one. -

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Decide whether or not the functions are inverses of each other. - f(x) =x+3,x≥−3;g(x) =x2+3f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3f(x) =x+3​,x≥−3;g(x) =x2+3

Correct AnswerverifiedShow Answer

Use the vertical line test to determine whether the graph represents a function. -

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Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x) =1x+3f ( x ) = \frac { 1 } { x + 3 }f(x) =x+31​

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The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(- 1, 0)

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The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?

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Solve the problem. -A cellular phone plan had the following schedule of charges: What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls.

Correct Answerverified $27.50 $32.50; \[C ( x ) = \left\{ \begi ...View AnswerShow Answer

Find the domain of the composite function f g. Write the domain in interval notation. - f(x) =8x+56,g(x) =x+6f ( x ) = 8 x + 56 , g ( x ) = x + 6f(x) =8x+56,g(x) =x+6

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Graph the function. -f(x) = -2

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Use the graph to determine the function's domain and range. Write the domain and range in interval notation. -

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Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x) =−∣x∣f(x) =-|x|f(x) =−∣x∣

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Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - y=2f(x) y=2 f(x) y=2f(x)

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Correct Answer
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Correct Answer
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For the given functions f and g, find the requested composite function. - $f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quad$ Find the function $f \circ g$ .

Correct Answer
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For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quad$ Find $\frac { f } { g }$

Correct Answer
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Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = | x - 3 | + 2$

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Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3$

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$27.50 $32.50; \[C ( x ) = \left\{ \begi ...
View Answer

Find the domain of the composite function f g. Write the domain in interval notation. - $f ( x ) = 8 x + 56 , g ( x ) = x + 6$

Correct Answer
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Correct Answer
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Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x) =-|x|$

Correct Answer
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Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - $y=2 f(x)$

Correct Answer
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