Question 1

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.
-domain of  f(x) =x+93f(x) =\sqrt[3]{x+9}f(x) =3x+9​

Accepted Answer

A)    [0,∞) [0, \infty) [0,∞)  
B)    [9,∞) [9, \infty) [9,∞)  
C)    (−∞,9](-\infty, 9](−∞,9] 
D)    (−9,∞) (-9, \infty) (−9,∞)  
E)    (−∞,∞) (-\infty, \infty) (−∞,∞)  F)   (9,∞) (9, \infty) (9,∞)  G)   (−∞,0](-\infty, 0](−∞,0] H)   [−9,∞) [-9, \infty) [−9,∞)

Question 2

Solve each of the following analytically, showing all steps. Next graph $y_{1}=|2 x-1|$ and $y_{2}=5$ in the standard viewing window of a graphing calculator. Then state how the graphs support your solution in each case.
(a) $|2 x-1|=5$
(b) $|2 x-1|5$

Accepted Answer

(a)

; the

-coordinates of the points o...

Question 3

Specialty Printing produces engraved wedding invitations. If $x$ represents the number of invitations, where $x>0$, then the function defined by $f(x)=75 \llbracket \frac{x}{25} \rrbracket+100$ gives the total cost in dollars.
(a) Using dot mode and the window $[0,250]$ by $[0,900]$, graph this function on a graphing calculator.
(b) Use the graph to find the cost of hiring Specialty Printing to print 120 invitations.

Accepted Answer

The answer of Specialty Printing produces engraved wedding invitations. If...

Question 4

Given $f(x)=4 x^{2}-3 x+2$ and $g(x)=3 x+2$, find each of the following. Simplify the expression when possible.
(a) $(f-g)(x)$
(b) $\frac{f}{g}(x)$
(c) the domain of $\frac{f}{g}$
(d) $(f \circ g)(x)$
(e) $\frac{f(x+h)-f(x)}{h}(h \neq 0)$

Accepted Answer

(a) <img loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> (b) <img loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> ...

Question 5

(a) Write a description that explains how the graph of $y=\sqrt[3]{x+5}$ can be obtained by translating the graph of $y=\sqrt[3]{x}$
(b) Sketch by hand the graph of $y=-|x-2|+3$. State the domain and the range.

Accepted Answer

(a) Shift the graph of <img loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> five u...

Question 6

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all
-range of  f(x) =∣x∣+3f(x) =|x|+3f(x) =∣x∣+3

Accepted Answer

A)    [3,∞) [3, \infty) [3,∞)  
B)    [0,∞) [0, \infty) [0,∞)  
C)    (3,∞) (3, \infty) (3,∞)  
D)    (−∞,0](-\infty, 0](−∞,0] 
E)    [−3,∞) [-3, \infty) [−3,∞)  F)   (−∞,3](-\infty, 3](−∞,3] G)   (−∞,∞) (-\infty, \infty) (−∞,∞)  H)   (−∞,0) (-\infty, 0) (−∞,0)

Question 7

The graph of $y=f(x)$ is shown here.
  
Sketch the graph of each of the following. Use ordered pairs to indicate 3 points on the graph.
(a) $y=f(x+3)$
(b) $y=f(x)+3$
(c) $y=f(-x)$
(d) $y=-f(x)$
(e) $y=3 f(x)$
(f) $y=|f(x)|$

Accepted Answer

(a) <img loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> (b)...

Question 8

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.
-domain of  x=y2+9x=y^{2}+9x=y2+9

Accepted Answer

A)    [0,∞) [0, \infty) [0,∞)  
B)    [9,∞) [9, \infty) [9,∞)  
C)    (−∞,9](-\infty, 9](−∞,9] 
D)    (−9,∞) (-9, \infty) (−9,∞)  
E)    (−∞,∞) (-\infty, \infty) (−∞,∞)  F)   (9,∞) (9, \infty) (9,∞)  G)   (−∞,0](-\infty, 0](−∞,0] H)   [−9,∞) [-9, \infty) [−9,∞)

Question 9

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.
-range of  f(x) =x+2f(x) =\sqrt{x+2}f(x) =x+2​

Accepted Answer

A)    (−∞,0) (-\infty, 0) (−∞,0)  
B)    (−∞,∞) (-\infty, \infty) (−∞,∞)  
C)    (−∞,2](-\infty, 2](−∞,2] 
D)    [−2,∞) [-2, \infty) [−2,∞)  
E)    (−∞,0](-\infty, 0](−∞,0] F)   (2,∞) (2, \infty) (2,∞)  G)   [0,∞) [0, \infty) [0,∞)  H)   [2,∞) [2, \infty) [2,∞)

Question 10

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.
-range of  f(x) =x3+5f(x) =\sqrt[3]{x}+5f(x) =3x​+5

Accepted Answer

A)    (−∞,∞) (-\infty, \infty) (−∞,∞)  
B)    [0,∞) [0, \infty) [0,∞)  
C)    (−∞,0](-\infty, 0](−∞,0] 
D)    [−5,∞) [-5, \infty) [−5,∞)  
E)    (5,∞) (5, \infty) (5,∞)  F)   (−5,∞) (-5, \infty) (−5,∞)  G)   (−∞,5](-\infty, 5](−∞,5] H)   [5,∞) [5, \infty) [5,∞)

Question 11

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.
-range of  f(x) =x−5f(x) =\sqrt{x-5}f(x) =x−5​

Accepted Answer

A)    (−∞,∞) (-\infty, \infty) (−∞,∞)  
B)    [0,∞) [0, \infty) [0,∞)  
C)    (−∞,0](-\infty, 0](−∞,0] 
D)    [−5,∞) [-5, \infty) [−5,∞)  
E)    (5,∞) (5, \infty) (5,∞)  F)   (−5,∞) (-5, \infty) (−5,∞)  G)   (−∞,5](-\infty, 5](−∞,5] H)   [5,∞) [5, \infty) [5,∞)

Question 12

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.
-range of  f(x) =∣x∣+9f(x) =|x|+9f(x) =∣x∣+9

Accepted Answer

A)    [0,∞) [0, \infty) [0,∞)  
B)    [9,∞) [9, \infty) [9,∞)  
C)    (−∞,9](-\infty, 9](−∞,9] 
D)    (−9,∞) (-9, \infty) (−9,∞)  
E)    (−∞,∞) (-\infty, \infty) (−∞,∞)  F)   (9,∞) (9, \infty) (9,∞)  G)   (−∞,0](-\infty, 0](−∞,0] H)   [−9,∞) [-9, \infty) [−9,∞)

Question 13

(a) Write a description that explains how the graph of $y=\sqrt[3]{x-4}+5$ can be obtained by translating the graph of $y=\sqrt[3]{x}$
(b) Sketch by hand the graph of $y=\frac{1}{2}|x-4|+3$. State the domain and the range.

Accepted Answer

(a) Shift the graph of <img loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> four u...

Question 14

Graph $y=f(x)$ by hand.
(a) $f(x)=\sqrt[3]{x}+1$
(b) $f(x)=|-2 x|$

Accepted Answer

The answer of Graph $y=f(x)$ by hand.
(a) $f(x)=\sqrt[3]{x}+1$
(b) $f(x)=|-2 x|$...

Question 15

Consider the graph of the function shown here.
  
State the interval(s) over which the function is:
(a) increasing
(b) decreasing
(c) constant
(d) continuous
(e) What is the domain of the function?
(f) What is the range of this function?

Accepted Answer

(a) <img loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> (b) <img loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> ...

Question 16

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.
-range of  x=y2−5x=y^{2}-5x=y2−5

Accepted Answer

A)    (−∞,∞) (-\infty, \infty) (−∞,∞)  
B)    [0,∞) [0, \infty) [0,∞)  
C)    (−∞,0](-\infty, 0](−∞,0] 
D)    [−5,∞) [-5, \infty) [−5,∞)  
E)    (5,∞) (5, \infty) (5,∞)  F)   (−5,∞) (-5, \infty) (−5,∞)  G)   (−∞,5](-\infty, 5](−∞,5] H)   [5,∞) [5, \infty) [5,∞)

Question 17

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.
-domain of  f(x) =x−53f(x) =\sqrt[3]{x-5}f(x) =3x−5​

Accepted Answer

A)    (−∞,∞) (-\infty, \infty) (−∞,∞)  
B)    [0,∞) [0, \infty) [0,∞)  
C)    (−∞,0](-\infty, 0](−∞,0] 
D)    [−5,∞) [-5, \infty) [−5,∞)  
E)    (5,∞) (5, \infty) (5,∞)  F)   (−5,∞) (-5, \infty) (−5,∞)  G)   (−∞,5](-\infty, 5](−∞,5] H)   [5,∞) [5, \infty) [5,∞)

Question 18

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.
-range of  f(x) =∣x+5∣f(x) =|x+5|f(x) =∣x+5∣

Accepted Answer

A)    (−∞,∞) (-\infty, \infty) (−∞,∞)  
B)    [0,∞) [0, \infty) [0,∞)  
C)    (−∞,0](-\infty, 0](−∞,0] 
D)    [−5,∞) [-5, \infty) [−5,∞)  
E)    (5,∞) (5, \infty) (5,∞)  F)   (−5,∞) (-5, \infty) (−5,∞)  G)   (−∞,5](-\infty, 5](−∞,5] H)   [5,∞) [5, \infty) [5,∞)

Question 19

Observe the coordinates displayed at the bottom of the given screen showing a portion of the graph $y=f(x)$. Answer each of the following based on your observation.
  
(a) If the graph is symmetric with respect to the $y$-axis, what are the coordinates of another point on the graph?
(b) If the graph is symmetric with respect to the origin, what are the coordinates of another point on the graph?
(c) Suppose the graph is symmetric with respect to the $y$-axis. Sketch a typical viewing window with dimensions $[-5,5]$ by $[0,10]$. Then draw the graph you would expect to see in this window.

Accepted Answer

The answer of Observe the coordinates displayed at the bottom...

Question 20

If the point $(4,3)$ lies on the graph of $y=f(x)$, determine a point on the graph of each equation.
(a) $y=2 f(x)$
(b) $y=f(2 x)-1$

Accepted Answer

The answer of If the point $(4,3)$ lies on the...

Exam 2: Analysis of Graphs of Functions

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $f(x) =\sqrt[3]{x}+5$

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -domain of $f(x) =\sqrt[3]{x-5}$

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $f(x) =\sqrt{x-5}$

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all -range of $f(x) =|x|+3$

Correct Answer
verified

Graph $y=f(x)$ by hand. (a) $f(x)=\sqrt[3]{x}+1$ (b) $f(x)=|-2 x|$

Correct Answer
verified

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $f(x) =\sqrt{x+2}$

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -domain of $x=y^{2}+9$

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $f(x) =|x|+9$

Correct Answer
verified

The graph of $y=f(x)$ is shown here. Sketch the graph of each of the following. Use ordered pairs to indicate 3 points on the graph. (a) $y=f(x+3)$ (b) $y=f(x)+3$ (c) $y=f(-x)$ (d) $y=-f(x)$ (e) $y=3 f(x)$ (f) $y=|f(x)|$

Correct Answer
verified
(a)

(b)...
View Answer

Given $f(x)=4 x^{2}-3 x+2$ and $g(x)=3 x+2$ , find each of the following. Simplify the expression when possible. (a) $(f-g)(x)$ (b) $\frac{f}{g}(x)$ (c) the domain of $\frac{f}{g}$ (d) $(f \circ g)(x)$ (e) $\frac{f(x+h)-f(x)}{h}(h \neq 0)$

Correct Answer
verified
(a)
(b)
...
View Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $x=y^{2}-5$

Correct Answer
verified

Solve each of the following analytically, showing all steps. Next graph $y_{1}=|2 x-1|$ and $y_{2}=5$ in the standard viewing window of a graphing calculator. Then state how the graphs support your solution in each case. (a) $|2 x-1|=5$ (b) $|2 x-1|<5$ (c) $|2 x-1|>5$

Correct Answer
verified

(a) ; the -coordinates of the points o...
View Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $f(x) =|x+5|$

Correct Answer
verified

(a) Write a description that explains how the graph of $y=\sqrt[3]{x-4}+5$ can be obtained by translating the graph of $y=\sqrt[3]{x}$ (b) Sketch by hand the graph of $y=\frac{1}{2}|x-4|+3$ . State the domain and the range.

Correct Answer
verified
(a) Shift the graph of four u...
View Answer

Correct Answer
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Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -domain of $f(x) =\sqrt[3]{x+9}$

Correct Answer
verified

If the point $(4,3)$ lies on the graph of $y=f(x)$ , determine a point on the graph of each equation. (a) $y=2 f(x)$ (b) $y=f(2 x)-1$

Correct Answer
verified

(a) Write a description that explains how the graph of $y=\sqrt[3]{x+5}$ can be obtained by translating the graph of $y=\sqrt[3]{x}$ (b) Sketch by hand the graph of $y=-|x-2|+3$ . State the domain and the range.

Correct Answer
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(a) Shift the graph of five u...
View Answer

Consider the graph of the function shown here. State the interval(s) over which the function is: (a) increasing (b) decreasing (c) constant (d) continuous (e) What is the domain of the function? (f) What is the range of this function?

Correct Answer
verified
(a)
(b)
...
View Answer

Exam 2: Analysis of Graphs of Functions

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of f(x) =x3+5f(x) =\sqrt[3]{x}+5f(x) =3x​+5

Correct AnswerverifiedShow Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -domain of f(x) =x−53f(x) =\sqrt[3]{x-5}f(x) =3x−5​

Correct AnswerverifiedShow Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of f(x) =x−5f(x) =\sqrt{x-5}f(x) =x−5​

Correct AnswerverifiedShow Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all -range of f(x) =∣x∣+3f(x) =|x|+3f(x) =∣x∣+3

Correct AnswerverifiedShow Answer

Graph y=f(x)y=f(x)y=f(x) by hand. (a) f(x)=x3+1f(x)=\sqrt[3]{x}+1f(x)=3x​+1 (b) f(x)=∣−2x∣f(x)=|-2 x|f(x)=∣−2x∣

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of f(x) =x+2f(x) =\sqrt{x+2}f(x) =x+2​

Correct AnswerverifiedShow Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -domain of x=y2+9x=y^{2}+9x=y2+9

Correct AnswerverifiedShow Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of f(x) =∣x∣+9f(x) =|x|+9f(x) =∣x∣+9

Correct AnswerverifiedShow Answer

Correct Answerverified(a) (b)...View AnswerShow Answer

Correct Answerverified(a) (b) ...View AnswerShow Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of x=y2−5x=y^{2}-5x=y2−5

Correct AnswerverifiedShow Answer

Correct Answerverified (a) ; the -coordinates of the points o...View AnswerShow Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of f(x) =∣x+5∣f(x) =|x+5|f(x) =∣x+5∣

Correct AnswerverifiedShow Answer

(a) Write a description that explains how the graph of y=x−43+5y=\sqrt[3]{x-4}+5y=3x−4​+5 can be obtained by translating the graph of y=x3y=\sqrt[3]{x}y=3x​ (b) Sketch by hand the graph of y=12∣x−4∣+3y=\frac{1}{2}|x-4|+3y=21​∣x−4∣+3 . State the domain and the range.

Correct Answerverified(a) Shift the graph of four u...View AnswerShow Answer

Correct AnswerverifiedShow Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -domain of f(x) =x+93f(x) =\sqrt[3]{x+9}f(x) =3x+9​

Correct AnswerverifiedShow Answer

If the point (4,3)(4,3)(4,3) lies on the graph of y=f(x)y=f(x)y=f(x) , determine a point on the graph of each equation. (a) y=2f(x)y=2 f(x)y=2f(x) (b) y=f(2x)−1y=f(2 x)-1y=f(2x)−1

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(a) Write a description that explains how the graph of y=x+53y=\sqrt[3]{x+5}y=3x+5​ can be obtained by translating the graph of y=x3y=\sqrt[3]{x}y=3x​ (b) Sketch by hand the graph of y=−∣x−2∣+3y=-|x-2|+3y=−∣x−2∣+3 . State the domain and the range.

Correct Answerverified(a) Shift the graph of five u...View AnswerShow Answer

Consider the graph of the function shown here. State the interval(s) over which the function is: (a) increasing (b) decreasing (c) constant (d) continuous (e) What is the domain of the function? (f) What is the range of this function?

Correct Answerverified(a) (b) ...View AnswerShow Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $f(x) =\sqrt[3]{x}+5$

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -domain of $f(x) =\sqrt[3]{x-5}$

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $f(x) =\sqrt{x-5}$

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all -range of $f(x) =|x|+3$

Correct Answer
verified

Graph $y=f(x)$ by hand. (a) $f(x)=\sqrt[3]{x}+1$ (b) $f(x)=|-2 x|$

Correct Answer
verified

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $f(x) =\sqrt{x+2}$

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -domain of $x=y^{2}+9$

Correct Answer
verified

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $f(x) =|x|+9$

Correct Answer
verified

Correct Answer
verified
(a)

(b)...
View Answer

Correct Answer
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(a)
(b)
...
View Answer

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $x=y^{2}-5$

Correct Answer
verified

Correct Answer
verified

(a) ; the -coordinates of the points o...
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Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -range of $f(x) =|x+5|$

Correct Answer
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(a) Write a description that explains how the graph of $y=\sqrt[3]{x-4}+5$ can be obtained by translating the graph of $y=\sqrt[3]{x}$ (b) Sketch by hand the graph of $y=\frac{1}{2}|x-4|+3$ . State the domain and the range.

Correct Answer
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(a) Shift the graph of four u...
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Correct Answer
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Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all. -domain of $f(x) =\sqrt[3]{x+9}$

Correct Answer
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If the point $(4,3)$ lies on the graph of $y=f(x)$ , determine a point on the graph of each equation. (a) $y=2 f(x)$ (b) $y=f(2 x)-1$

Correct Answer
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(a) Write a description that explains how the graph of $y=\sqrt[3]{x+5}$ can be obtained by translating the graph of $y=\sqrt[3]{x}$ (b) Sketch by hand the graph of $y=-|x-2|+3$ . State the domain and the range.

Correct Answer
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(a) Shift the graph of five u...
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Correct Answer
verified
(a)
(b)
...
View Answer