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

Accepted Answer

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

Question 2

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.

Accepted Answer

(a) $(-2,6)$
(b) $(-2,-6)$
(c)

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

Accepted Answer

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

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 $x=y^{2}+3$

Accepted Answer

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

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

Accepted Answer

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

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

Accepted Answer

A)  $(-\infty, \infty)$ 
B)  $[0, \infty)$ 
C)  $(-\infty, 0]$ 
D)  $[-5, \infty)$ 
E)  $(5, \infty)$
F) $(-5, \infty)$
G) $(-\infty, 5]$
H) $[5, \infty)$ 
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 7

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all
-range of $f(x)=(x-3)^{2}$

Accepted Answer

A)  $[3, \infty)$ 
B)  $[0, \infty)$ 
C)  $(3, \infty)$ 
D)  $(-\infty, 0]$ 
E)  $[-3, \infty)$
F) $(-\infty, 3]$
G) $(-\infty, \infty)$
H) $(-\infty, 0)$ 
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 $x=y^{2}+2$

Accepted Answer

A)  $(-\infty, 0)$ 
B)  $(-\infty, \infty)$ 
C)  $(-\infty, 2]$ 
D)  $[-2, \infty)$ 
E)  $(-\infty, 0]$
F) $(2, \infty)$
G) $[0, \infty)$
H) $[2, \infty)$ 
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 9

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

Accepted Answer

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

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) @#LAT-DLM&
(b) @#LAT-DLM&

Question 11

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

Accepted Answer

(a) @#LAT-DLM&
(b) @#LAT-DLM&

Question 12

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.

Accepted Answer

(a) @#LAT-DLM&
(b) @#LAT-DLM&
(c) @#LAT-DLM&
(d) @#LAT-DLM&

Question 13

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 14

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

Accepted Answer

A)  $[3, \infty)$ 
B)  $[0, \infty)$ 
C)  $(3, \infty)$ 
D)  $(-\infty, 0]$ 
E)  $[-3, \infty)$
F) $(-\infty, 3]$
G) $(-\infty, \infty)$
H) $(-\infty, 0)$ 
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 15

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.

Accepted Answer

(a) @#LAT-DLM&
(b) @#LAT-DLM&
(c) @#LAT-DLM&
(d) 1

Question 16

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.

Accepted Answer

The answer of Royal Tree Service has been hired to...

Question 17

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

Accepted Answer

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

Question 18

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.

Accepted Answer

(a) @#LAT-DLM&
(b) @#LAT-DLM&
(c) @#LAT-DLM&
(d) 2

Question 19

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) $|3 x-6|3$

Accepted Answer

@#IMG-DLM& 
(a) @#LAT-DLM&; the @#LAT-DLM&-coordinates of the points o

Question 20

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 $[-10,10]$.

Accepted Answer

The answer of Consider the piecewise-defined function defined by \(f(x)=\left\{\begin{array}{ll}x^{2}-7...

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

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

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all -domain of $x=y^{2}+3$

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

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

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all -range of $f(x)=(x-3)^{2}$

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

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

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?

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

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

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

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) $|3 x-6|>3$

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 $[-10,10]$ .

Linear Functions, Equations, and Inequalities

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Limits, Derivatives, and Definite Integrals

Reference: Basic Algebraic Concepts

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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. -domain of f(x)=x+5f(x)=\sqrt{x}+5f(x)=x​+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)=x−2f(x)=\sqrt{x}-2f(x)=x​−2

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+3x=y^{2}+3x=y2+3

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

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)=x2−5f(x)=x^{2}-5f(x)=x2−5

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)2f(x)=(x-3)^{2}f(x)=(x−3)2

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+2x=y^{2}+2x=y2+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)=3−xf(x)=\sqrt{3-x}f(x)=3−x​

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?

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∣f(x)=|x-3|f(x)=∣x−3∣

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

Linear Functions, Equations, and Inequalities

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Limits, Derivatives, and Definite Integrals

Reference: Basic Algebraic Concepts

Filters

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

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

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all -domain of $x=y^{2}+3$

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

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

Match the set described with the correct interval notation. Choices may be used once, more than once, or not at all -range of $f(x)=(x-3)^{2}$

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

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

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

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