Question 1

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) $y=f(4 x)$

Accepted Answer

The answer of If the point $(2,7)$ lies on the...

Question 2

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

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 3

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

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 4

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

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

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) $|2 x+3|3$

Accepted Answer

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

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

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 7

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.

Accepted Answer

The answer of Rent and Go car rental serves the...

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

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 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?

Accepted Answer

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

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

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 11

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) $y=f(x)-3$

Accepted Answer

The answer of If the point $(4,2)$ lies on the...

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

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 13

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

The answer of The graph of $y=f(x)$ is shown here.
...

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 $x=y^{2}-5$

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 15

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

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 16

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

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 17

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

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 18

Tiny Toys is going to produce a toy race car version of the new Volkswagen Bug. The overhead for the project is $\$ 378$. Each toy Bug costs $\$ 1.25$ to make.
(a) Write a cost function $C$, where $x$ represents the number of toy Bugs manufactured.
(b) Find the revenue function $R$, if each toy Bug in part (a) sells for $\$ 3.00$.
(c) Give the profit function $P$.
(d) How many toy Bugs must be produced and sold before Tiny Toys 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

(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.

Accepted Answer

(a) Shift the graph of @#LAT-DLM& three

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

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) $(-\infty, 0)$

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) $y=f(4 x)$

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

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

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

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) $|2 x+3|>3$

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

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

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

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) $y=f(x)-3$

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

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

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

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

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) 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.

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

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

If the point (2,7)(2,7)(2,7) 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=f(12x)y=f\left(\frac{1}{2} x\right)y=f(21​x) (b) y=f(4x)y=f(4 x)y=f(4x)

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)=x2−5f(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. -domain 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 x=y2+3x=y^{2}+3x=y2+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+2f(x)=x^{2}+2f(x)=x2+2

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∣f(x)=|x-2|f(x)=∣x−2∣

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

If the point (4,2)(4,2)(4,2) 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=f(x−3)y=f(x-3)y=f(x−3) (b) y=f(x)−3y=f(x)-3y=f(x)−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)=x3−2f(x)=\sqrt[3]{x}-2f(x)=3x​−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=y2−5x=y^{2}-5x=y2−5

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+9x=y^{2}+9x=y2+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)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. -domain of f(x)=∣x−9∣f(x)=|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)=3−xf(x)=3-\sqrt{x}f(x)=3−x​

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

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) $y=f(4 x)$

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

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

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

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

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

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

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) $y=f(x)-3$

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

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

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

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

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

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