Deck 2: Analysis of Graphs of Functions

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 $f(x)=(x-3)^{2}$

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

Answer 1

$(-\infty, \infty)$

Question 2

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all

-range of $f(x)=(x-3)^{2}$

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

Answer 2

$[0, \infty)$

Question 3

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all

-domain of $x=y^{2}+3$

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

Answer 3

$[3, \infty)$

Question 4

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all

-range of $x=y^{2}+3$

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

Question 5

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all

-domain of $f(x)=3-\sqrt{x}$

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

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

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

Question 7

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all

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

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

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

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

Question 9

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all

-domain of $f(x)=|x-3|$

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

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 $f(x)=|x|+3$

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

Question 11

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) $y=|f(x)|$

Question 12

If the point $(2,7)$ lies on the graph of $y=f(x)$ , determine a point on the graph of each equation.
(a) $y=f\left(\frac{1}{2} x\right)$
(b) $y=f(4 x)$

Question 13

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

Question 14

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.

Question 15

(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.

Question 16

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?

Question 17

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) $|4 x+2|>2$

Question 18

Given $f(x)=3 x^{2}-2 x-6$ and $g(x)=3 x+5$ , 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) $\frac{f(x+h)-f(x)}{h}(h \neq 0)$

Question 19

Consider the piecewise-defined function defined by $f(x)=\left\{\begin{array}{ll}x^{2}-6 & \text { if } x \leq 1 \\ \sqrt{x} & \text { if } x>1\end{array}\right.$ .
(a) Graph $f$ by hand.
(b) Use a graphing calculator to obtain an accurate graph in the window $[-5,10]$ by $[-10,10]$ .

Question 20

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.

Question 21

Craig Mallery's band wants to record a CD. The cost to record a CD is $\$ 750$ for studio fees plus $\$ 4.50$ for each CD produced.
(a) Write a cost function $C$ , where $x$ represents the number of CDs produced.
(b) Find the revenue function $R$ , if each $\mathrm{CD}$ in part (a) sells for $\$ 12.00$ .
(c) Give the profit function $P$ .
(d) How many CDs must be produced and sold before the band earns a profit?
(e) Support the results of part (d) graphically.

Question 22

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $f(x)=x^{2}-5$

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

Question 23

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $f(x)=x^{2}-5$

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

Question 24

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $f(x)=\sqrt{x}+5$

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

Question 25

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $f(x)=\sqrt{x-5}$

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

Question 26

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $f(x)=|x|-5$

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

Question 27

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $f(x)=|x+5|$

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

Question 28

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $f(x)=\sqrt[3]{x-5}$

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

Question 29

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $f(x)=\sqrt[3]{x}+5$

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

Question 30

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $x=y^{2}-5$

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

Question 31

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $x=y^{2}-5$

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

Question 32

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) $y=|f(x)|$

Question 33

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

Question 34

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

Question 35

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 $[-8,8]$ by $[0,10]$ . Then draw the graph you would expect to see in this window.

Question 36

(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.

Question 37

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?

Question 38

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) $|2 x-1|>5$

Question 39

Given $f(x)=2 x^{2}+5 x-3$ and $g(x)=2 x+1$ , 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) $\frac{f(x+h)-f(x)}{h}(h \neq 0)$

Question 40

Consider the piecewise-defined function defined by $f(x)=\left\{\begin{array}{ll}x^{2}-7 & \text { if } x \leq 1 \\ -\sqrt{x}+5 & \text { if } x>1\end{array}\right.$ .
(a) Graph $f$ by hand.
(b) Use a graphing calculator to obtain an accurate graph in the window $[-5,10]$ by $[-10,10]$ .

Question 41

Royal Tree Service has been hired to clear an area of trees. If $x$ represents the number of hours they will work, where $x>0$ , then the function defined by $f(x)=125 \llbracket x \rrbracket+250$ gives the total cost in dollars.
(a) Using dot mode and the window $[0,10]$ by $[0,1500]$ , graph this function on a graphing calculator.
(b) Use the graph to find the cost of a 7.5 hour workday.

Question 42

Martin Boggs opens a new fruit juice shop that specializes in frozen blended juice drinks called "smoothies." His initial cost is $\$ 5075$ . Each smoothie costs $\$ 2.00$ to make.
(a) Write a cost function $C$ , where $x$ represents the number of smoothies made.
(b) Find the revenue function $R$ , if each smoothie in part (a) sells for $\$ 3.75$ .
(c) Give the profit function $P$ .
(d) How many smoothies must be made and sold before Martin earns a profit?
(e) Support the results of part (d) graphically.

Question 43

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $f(x)=\sqrt{x}-2$

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

Question 44

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $f(x)=\sqrt{x+2}$

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

Question 45

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $f(x)=|x-2|$

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

Question 46

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

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

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

Question 47

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $f(x)=x^{2}+2$

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

Question 48

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $f(x)=x^{2}+2$

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

Question 49

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

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

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

Question 50

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $f(x)=\sqrt[3]{x}-2$

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

Question 51

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $x=y^{2}+2$

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

Question 52

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $x=y^{2}+2$

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

Question 53

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) $y=|f(x)|$

Question 54

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

Question 55

Graph $y=f(x)$ by hand.
(a) $f(x)=-(x+1)^{2}+2$
(b) $f(x)=(x-3)^{2}-3$

Question 56

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.

Question 57

(a) Write a description that explains how the graph of $f(x)=\frac{1}{2} \sqrt[3]{x+3}$ can be obtained by translating the graph of $y=\sqrt[3]{x}$ .
(b) Sketch by hand the graph of $y=-3|x-6|+4$ . State the domain and the range.

Question 58

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?

Question 59

Solve each of the following analytically, showing all steps. Next graph $y_{1}=|3 x-6|$ and $y_{2}=3$ in the standard viewing window of a graphing calculator. Then state how the graphs support your solution in each case.
(a) $|3 x-6|=3$
(b) $|3 x-6|<3$
(c) $|3 x-6|>3$

Question 60

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) $\frac{f(x+h)-f(x)}{h}(h \neq 0)$

Question 61

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 $[-10,20]$ .

Question 62

Rent and Go car rental serves the greater Sacramento area. If $x$ represents the number of days you rent a car, where $x>0$ , then the function defined by $f(x)=30 \llbracket x \rrbracket+10$ gives the total cost of a car rental in dollars.
(a) Using dot mode and the window $[0,6]$ by $[0,200]$ , graph this function on a graphing calculator.
(b) Use the graph to find the cost of renting a car for 5 days.

Question 63

The Class of 2010 wants to raise money for a class trip by selling hot pretzels in school. The initial cost is $\$ 160$ to rent the oven. Each pretzel costs $\$ .75$ to make.
(a) Write a cost function $C$ , where $x$ represents the number of pretzels made.
(b) Find the revenue function $R$ , if each pretzel in part (a) sells for $\$ 2.00$ .
(c) Give the profit function $P$ .
(d) How many pretzels must be made and sold before the class earns a profit?
(e) Support the results of part (d) graphically.

Question 64

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

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

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

Question 65

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

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

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

Question 66

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

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

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

Question 67

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

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

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

Question 68

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $f(x)=|x-9|$

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

Question 69

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $f(x)=|x|+9$

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

Question 70

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

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

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

Question 71

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

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

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

Question 72

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-domain of $x=y^{2}+9$

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

Question 73

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all.

-range of $x=y^{2}+9$

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

Question 74

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) $y=|f(x)|$

Question 75

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) $y=f(2 x)-1$

Question 76

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

Question 77

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.

Question 78

(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.

Question 79

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?

Question 80

Solve each of the following analytically, showing all steps. Next graph $y_{1}=|2 x+3|$ and $y_{2}=3$ in the standard viewing window of a graphing calculator. Then state how the graphs support your solution in each case.
(a) $|2 x+3|=3$
(b) $|2 x+3|<3$
(c) $|2 x+3|>3$