Question 1

Consider the piecewise-defined function defined by $f(x)=\left\{\begin{array}{ll}4 \sqrt{-x}+2 & \text { if } x<-4 \ .5 x^{2}-6 & \text { if } x \geq-4\end{array}\right.$.
(a) Graph $f$ by hand.
(b) Use a graphing calculator to obtain an accurate graph in the window $[-15,10]$ by $[-10,20]$.

Accepted Answer

The answer of Consider the piecewise-defined function defined by \(f(x)=\left\{\begin{array}{ll}4...

Question 2

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) $y=f(x+2)$
(b) $y=f(x)+2$
(c) $y=f(-x)$
(d) $y=-f(x)$
(e) $y=2 f(x)$
(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 3

In Fairfield you can go to a coffee shop and pay to use their Internet service. If $x$ represents the number of minutes you are online, where $x>0$, then the function defined by $f(x)=.50 \llbracket x \rrbracket+1.50$ gives the total cost in dollars.
(a) Using dot mode and the window $[0,15]$ by $[0,10]$, graph this function on a graphing calculator.
(b) Use the graph to find the cost of being online for 6.5 minutes.

Accepted Answer

The answer of In Fairfield you can go to a...

Question 4

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) =x2+9f(x) =x^{2}+9f(x) =x2+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 5

(a) Write a description that explains how the graph of $y=2 \sqrt{x-1}+3$ can be obtained by translating the graph of $y=\sqrt{x}$.
(b) Sketch by hand the graph of $y=-2|x+2|-3$. 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"> one un...

Question 6

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−9f(x) =\sqrt{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 7

Consider the piecewise-defined function defined by $f(x)=\left\{\begin{array}{ll}x^{2}-8 & \text { if } x<4 \ -2 \bar{x}-4 & \text { if } x \geq 4\end{array}\right.$.
(a) Graph $f$ by hand.
(b) Use a graphing calculator to obtain an accurate graph in the window $[-5,15]$ by $[-10,5]$.

Accepted Answer

The answer of Consider the piecewise-defined function defined by \(f(x)=\left\{\begin{array}{ll}x^{2}-8...

Question 8

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) =x3−9f(x) =\sqrt[3]{x}-9f(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 9

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 $[-6,6]$ 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 10

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∣−5f(x) =|x|-5f(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 11

Solve each of the following analytically, showing all steps. Next graph $y_{1}=|4 x+2|$ and $y_{2}=2$ in the standard viewing window of a graphing calculator. Then state how the graphs support your solution in each case.
(a) $|4 x+2|=2$
(b) $|4 x+2|2$

Accepted Answer

(a)

; the

-coordinates of the points o...

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) =\sqrt{x+9}f(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

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) =x3−3f(x) =\sqrt[3]{x}-3f(x) =3x​−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 14

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 15

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) =|x|+2f(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 16

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+33f(x) =\sqrt[3]{x+3}f(x) =3x+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 17

Given $f(x)=-2 x^{2}+2 x-1$ and $g(x)=2 x-3$, 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 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) =x2+9f(x) =x^{2}+9f(x) =x2+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 19

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 20

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+23f(x) =\sqrt[3]{x+2}f(x) =3x+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,∞)

Exam 2: Analysis of Graphs of Functions

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
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(a)
(b)
...
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Consider the piecewise-defined function defined by $f(x)=\left\{\begin{array}{ll}4 \sqrt{-x}+2 & \text { if } x<-4 \\ .5 x^{2}-6 & \text { if } x \geq-4\end{array}\right.$ . (a) Graph $f$ by hand. (b) Use a graphing calculator to obtain an accurate graph in the window $[-15,10]$ by $[-10,20]$ .

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 $f(x) =x^{2}+9$

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 -range of $f(x) =\sqrt[3]{x}-3$

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 $f(x) =x^{2}+9$

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 $f(x) =\sqrt{x+9}$

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 $f(x) =|x|+2$

Correct Answer
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Consider the piecewise-defined function defined by $f(x)=\left\{\begin{array}{ll}x^{2}-8 & \text { if } x<4 \\ -2 \bar{x}-4 & \text { if } x \geq 4\end{array}\right.$ . (a) Graph $f$ by hand. (b) Use a graphing calculator to obtain an accurate graph in the window $[-5,15]$ by $[-10,5]$ .

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 $f(x) =\sqrt[3]{x+2}$

Correct Answer
verified

Solve each of the following analytically, showing all steps. Next graph $y_{1}=|4 x+2|$ and $y_{2}=2$ in the standard viewing window of a graphing calculator. Then state how the graphs support your solution in each case. (a) $|4 x+2|=2$ (b) $|4 x+2|<2$ (c) $|4 x+2|>2$

Correct Answer
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(a) ; the -coordinates of the points o...
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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) $y=f(x+2)$ (b) $y=f(x)+2$ (c) $y=f(-x)$ (d) $y=-f(x)$ (e) $y=2 f(x)$ (f) $y=|f(x)|$

Correct Answer
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(a)
(b) ...
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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 $f(x) =\sqrt[3]{x+3}$

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 $f(x) =\sqrt{x}-9$

Correct Answer
verified

Correct Answer
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Given $f(x)=-2 x^{2}+2 x-1$ and $g(x)=2 x-3$ , 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) $\frac{f(x+h)-f(x)}{h}(h \neq 0)$

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(a)
(b)
...
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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
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(a)

(b)...
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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 $f(x) =|x|-5$

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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 $f(x) =\sqrt[3]{x}-9$

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

Correct Answer
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(a) Shift the graph of one un...
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Exam 2: Analysis of Graphs of Functions

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

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) =x2+9f(x) =x^{2}+9f(x) =x2+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) =x3−3f(x) =\sqrt[3]{x}-3f(x) =3x​−3

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) =x2+9f(x) =x^{2}+9f(x) =x2+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) =\sqrt{x+9}f(x) =x+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∣+2f(x) =|x|+2f(x) =∣x∣+2

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. -domain of f(x) =x+23f(x) =\sqrt[3]{x+2}f(x) =3x+2​

Correct AnswerverifiedShow Answer

Correct Answerverified (a) ; the -coordinates of the points o...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 -domain of f(x) =x+33f(x) =\sqrt[3]{x+3}f(x) =3x+3​

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−9f(x) =\sqrt{x}-9f(x) =x​−9

Correct AnswerverifiedShow Answer

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. -domain of f(x) =∣x∣−5f(x) =|x|-5f(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) =x3−9f(x) =\sqrt[3]{x}-9f(x) =3x​−9

Correct AnswerverifiedShow Answer

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

Correct Answerverified(a) Shift the graph of one un...View AnswerShow Answer

Correct Answer
verified
(a)
(b)
...
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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 $f(x) =x^{2}+9$

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 -range of $f(x) =\sqrt[3]{x}-3$

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 $f(x) =x^{2}+9$

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 $f(x) =\sqrt{x+9}$

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. -range of $f(x) =|x|+2$

Correct Answer
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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 $f(x) =\sqrt[3]{x+2}$

Correct Answer
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Correct Answer
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(a) ; the -coordinates of the points o...
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Correct Answer
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(a)
(b) ...
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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 $f(x) =\sqrt[3]{x+3}$

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 $f(x) =\sqrt{x}-9$

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

(b)...
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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 $f(x) =|x|-5$

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. -range of $f(x) =\sqrt[3]{x}-9$

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

Correct Answer
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(a) Shift the graph of one un...
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