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Applied Algebra:
Modeling and functions
compiled by Sean Laverty on behalf of others, Katherine Yoshiwara
Contents
Index
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Contents
Prev
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Front Matter
Colophon
Preface
1
Functions and Their Graphs
Linear Models
Functions
Graphs of Functions
Slope and Rate of Change
Linear Functions
Chapter Summary and Review
Projects for Chapter 1
2
Modeling with Functions
Nonlinear Models
Some Basic Functions
Transformations of Graphs
Functions as Mathematical Models
The Absolute Value Function
Domain and Range
Chapter Summary and Review
Projects for Chapter 2: Periodic Functions
3
Power Functions
Variation
Integer Exponents
Roots and Radicals
Rational Exponents
Chapter Summary and Review
Projects for Chapter 3
4
Exponential Functions
Exponential Growth and Decay
Exponential Functions
Logarithms
Properties of Logarithms
Exponential Models
Chapter Summary and Review
Projects for Chapter 4
5
Logarithmic Functions
Inverse Functions
Logarithmic Functions
The Natural Base
Logarithmic Scales
Chapter Summary and Review
Projects for Chapter 5
6
Quadratic Functions
Factors and \(x\)-Intercepts
Solving Quadratic Equations
Graphing Parabolas
Problem Solving
Chapter Summary and Review
Projects for Chapter 6
7
Polynomial and Rational Functions
Polynomial Functions
Graphing Polynomial Functions
Complex Numbers
Graphing Rational Functions
Equations That Include Algebraic Fractions
Chapter Summary and Review
Projects for Chapter 7
8
Data and functions
Linear Regression
Curve Fitting
Appendices
A
Algebra Skills Refresher
Numbers and Operations
Linear Equations and Inequalities
Algebraic Expressions and Problem Solving
Graphs and Equations
Linear Systems in Two Variables
Laws of Exponents
Polynomials and Factoring
Factoring Quadratic Trinomials
Working with Algebraic Fractions
Working with Radicals
Facts from Geometry
Properties of Lines
The Real Number System
B
Using a Graphing Calculator
Getting Started
Entering Expressions
Editing Expressions
Graphing an Equation
Making a Table
Regression
Function Notation and Transformation of Graphs
C
Glossary
D
Technology (Graphing calculators)
E
Geometry formulas
F
Answers to Selected Exercises
G
GNU Free Documentation License
Bibliography
Index
Colophon
Authored in PreTeXt
Solutions
F
Answers to Selected Exercises
Chapter
1
Functions and Their Graphs
¶
Section
1.1
Linear Models
¶
Exercises
Homework 1.1
¶
1
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Answer
3
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Answer
5
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Answer
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Section
1.2
Functions
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Exercises
Homework 1.2
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1
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Answer
3
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5
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7
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Section
1.3
Graphs of Functions
¶
Exercises
Homework 1.3
¶
1
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Answer
3
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5
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7
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Section
1.4
Slope and Rate of Change
¶
Exercises
Homework 1.4
¶
1
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Answer
3
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Answer
5
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Answer
7
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Section
1.5
Linear Functions
¶
Exercises
Homework 1.5
¶
1
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Answer
3
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Answer
5
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Answer
7
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Section
1.6
Chapter Summary and Review
¶
Exercises
Chapter 1 Review Problems
¶
1
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Answer
3
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Answer
5
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Answer
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Chapter
2
Modeling with Functions
¶
Section
2.1
Nonlinear Models
¶
Exercises
Homework 2.1
¶
1
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Answer
3
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Answer
5
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Answer
7
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11
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Section
2.2
Some Basic Functions
¶
Exercises
Homework 2.2
¶
1
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Answer
3
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Answer
5
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Answer
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Section
2.3
Transformations of Graphs
¶
Exercises
Homework 2.3
¶
1
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Answer
3
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Answer
5
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Answer
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Section
2.4
Functions as Mathematical Models
¶
Exercises
Homework 2.4
¶
1
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Answer
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Section
2.5
The Absolute Value Function
¶
Exercises
Homework 2.5
¶
1
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Answer
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Section
2.6
Domain and Range
¶
Exercises
Homework 2.6
¶
1
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Section
2.7
Chapter Summary and Review
¶
Exercises
Chapter 2 Review Problems
¶
1
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Answer
3
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Chapter
3
Power Functions
¶
Section
3.1
Variation
¶
Exercises
Homework 3.1
¶
1
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Answer
3
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Answer
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Answer
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Section
3.2
Integer Exponents
¶
Exercises
Homework 3.2
¶
1
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Answer
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Section
3.3
Roots and Radicals
¶
Exercises
Homework 3.3
¶
1
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Section
3.4
Rational Exponents
¶
Exercises
Homework 3.4
¶
1
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Section
3.5
Chapter Summary and Review
¶
Exercises
Chapter 3 Review Problems
¶
1
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Answer
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Chapter
4
Exponential Functions
¶
Section
4.1
Exponential Growth and Decay
¶
Exercises
Homework 4.1
¶
1
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Answer
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Section
4.2
Exponential Functions
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Exercises
Homework 4.2
¶
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Answer
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Section
4.3
Logarithms
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Exercises
Homework 4.3
¶
1
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Answer
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Section
4.4
Properties of Logarithms
¶
Exercises
Homework 4.4
¶
1
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Answer
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Answer
67
.
Answer
Section
4.5
Exponential Models
¶
Exercises
Homework 4.5
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
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Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
Section
4.6
Chapter Summary and Review
¶
Exercises
Chapter 4 Review Problems
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
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Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
61
.
Answer
63
.
Answer
65
.
Answer
67
.
Answer
69
.
Answer
71
.
Answer
73
.
Answer
75
.
Answer
77
.
Answer
79
.
Answer
81
.
Answer
Chapter
5
Logarithmic Functions
¶
Section
5.1
Inverse Functions
¶
Exercises
Homework 5.1
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
Section
5.2
Logarithmic Functions
¶
Exercises
Homework 5.2
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
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Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
61
.
Answer
63
.
Answer
65
.
Answer
67
.
Answer
69
.
Answer
71
.
Answer
Section
5.3
The Natural Base
¶
Exercises
Homework 5.3
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
Section
5.4
Logarithmic Scales
¶
Exercises
Homework 5.4
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
Section
5.5
Chapter Summary and Review
¶
Exercises
Chapter 5 Review Problems
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
61
.
Answer
63
.
Answer
65
.
Answer
67
.
Answer
69
.
Answer
Chapter
6
Quadratic Functions
¶
Section
6.1
Factors and \(x\)-Intercepts
¶
Exercises
Homework 6.1
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
61
.
Answer
63
.
Answer
Section
6.2
Solving Quadratic Equations
¶
Exercises
Homework 6.2
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
61
.
Answer
63
.
Answer
65
.
Answer
67
.
Answer
69
.
Answer
Section
6.3
Graphing Parabolas
¶
Exercises
Homework 6.3
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
Section
6.4
Problem Solving
¶
Exercises
Homework 6.4
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
Section
6.5
Chapter Summary and Review
¶
Exercises
Chapter 6 Review Problems
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
61
.
Answer
63
.
Answer
65
.
Answer
67
.
Answer
69
.
Answer
71
.
Answer
73
.
Answer
75
.
Answer
77
.
Answer
79
.
Answer
81
.
Answer
83
.
Answer
85
.
Answer
87
.
Answer
Chapter
7
Polynomial and Rational Functions
¶
Section
7.1
Polynomial Functions
¶
Exercises
Homework 7.1
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
61
.
Answer
63
.
Answer
Section
7.2
Graphing Polynomial Functions
¶
Exercises
Homework 7.2
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
61
.
Answer
63
.
Answer
65
.
Answer
67
.
Answer
69
.
Answer
Section
7.3
Complex Numbers
¶
Exercises
Homework 7.3
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
61
.
Answer
63
.
Answer
65
.
Answer
67
.
Answer
69
.
Answer
71
.
Answer
Section
7.4
Graphing Rational Functions
¶
Exercises
Homework 7.4
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
Section
7.5
Equations That Include Algebraic Fractions
¶
Exercises
Homework 7.5
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
Section
7.6
Chapter Summary and Review
¶
Exercises
Chapter 7 Review Problems
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
41
.
Answer
43
.
Answer
45
.
Answer
47
.
Answer
49
.
Answer
51
.
Answer
53
.
Answer
55
.
Answer
57
.
Answer
59
.
Answer
61
.
Answer
63
.
Answer
65
.
Answer
67
.
Answer
69
.
Answer
71
.
Answer
73
.
Answer
75
.
Answer
77
.
Answer
79
.
Answer
81
.
Answer
83
.
Answer
Chapter
8
Data and functions
¶
Section
8.1
Linear Regression
¶
Exercises
Homework 1.6
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
39
.
Answer
Section
8.2
Curve Fitting
¶
Exercises
Homework 6.6
¶
1
.
Answer
3
.
Answer
5
.
Answer
7
.
Answer
9
.
Answer
11
.
Answer
13
.
Answer
15
.
Answer
17
.
Answer
19
.
Answer
21
.
Answer
23
.
Answer
25
.
Answer
27
.
Answer
29
.
Answer
31
.
Answer
33
.
Answer
35
.
Answer
37
.
Answer
