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

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 2

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

Accepted Answer

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

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 5

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 6

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

Accepted Answer

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

Question 8

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

Question 9

(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 @#LAT-DLM& one un

Question 10

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-DLM& 
(b)

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

Accepted Answer

A)  $[0, \infty)$ 
B)  $[9, \infty)$ 
C)  $(-\infty, 9]$ 
D)  $(-9, \infty)$ 
E)  $(-\infty, \infty)$
F) $(9, \infty)$
G) $(-\infty, 0]$
H) $[-9, \infty)$ 
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 12

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

Accepted Answer

A)  $[0, \infty)$ 
B)  $[9, \infty)$ 
C)  $(-\infty, 9]$ 
D)  $(-9, \infty)$ 
E)  $(-\infty, \infty)$
F) $(9, \infty)$
G) $(-\infty, 0]$
H) $[-9, \infty)$ 
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 13

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

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 14

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 15

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

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 16

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

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 17

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

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 18

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

Accepted Answer

A)  $[0, \infty)$ 
B)  $[9, \infty)$ 
C)  $(-\infty, 9]$ 
D)  $(-9, \infty)$ 
E)  $(-\infty, \infty)$
F) $(9, \infty)$
G) $(-\infty, 0]$
H) $[-9, \infty)$ 
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 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) @#LAT-DLM&
(b) @#LAT-DLM&

Question 20

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

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

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

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

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 $[-10,5]$ .

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

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) $y=|f(x)|$

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

(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.

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) $y=|f(x)|$

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

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

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

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 $[-10,20]$ .

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

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

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

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

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?

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) $|4 x+2|>2$

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

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

(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.

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​

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

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​

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​

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

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

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

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?

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

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

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

(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.

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

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

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

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

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

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

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