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College Algebra
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Contents
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I
Functions and Function Notation
1
Preliminaries
Plotting Points and the Coordinate Plane
Intercepts
Order of Operations and Simplifying
Solving Equations
2
Function Notation
Evaluating Functions from a Formula
Piecewise Functions
Functions as Graphs and Tables
Algebra with Functions
Solving with Functions
3
Composition
Evaluating a Composition of Functions
Simplifying a Composition of Functions
4
Inverse Functions
Evaluating Inverse Functions
Finding a Formula for the Inverse
5
Standard 1 Review
Summary of Notes
Practice Quizzes
II
Linear Functions
6
Linear Functions
Slope of a Line
Equation of a Line
Linear Models
7
Systems of Linear Equations
Solutions to a System of Equations
Solving a System of Equations: Substitution
Solving a System of Equations: Elimination
Special Cases of Systems of Equations
8
Rate of Change
Computing Average Rate of Change
Difference Quotient
9
(*)Standard 2 Review
(*)Summary of Notes
Practice Quizzes
(*)Study Materials
III
Properties of Functions
10
Domain and Range
Interval Notation
Domain from a Graph
Range from a Graph
Domain from a Formula
11
Transformations
Vertical Shifts
Horizontal Shifts
Vertical Scales
Horizontal Scales
Reflections
Combining Transformations
Domain and Range of Transformations
12
(*)Standard 3 Review
(*)Summary of Notes
Practice Quizzes
(*)Study Materials
IV
Polynomial and Rational Functions
13
Quadratic Functions
Roots of Quadratic Functions
Equations of Quadaratic Functions
14
Polynomial Functions
Roots of Polynomials
Equation of Polynomials
End Behavior of Polynomials
15
Rational Functions
Domain of Rational Functions
End Behavior of Rational Functions
16
(*)Standard 4 Review
(*)Summary of Notes
Practice Quizzes
(*)Study Materials
V
Exponential and Logarithmic Functions
17
Exponential Functions
Equations of Exponential Functions
Graphs and End Behavior of Exponential Functions
The Number
\(e\)
18
Logarithmic Functions
Evaluating Logarithmic Functions
Graphs of Logarithmic Functions
The Natural Log
19
(*)Standard 5 Review
(*)Summary of Notes
Practice Quizzes
(*)Study Materials
VI
Exponential and Logarithmic Equations
20
Logarithm Properties
Combining Logarithms
Expanding Logarithms
21
Exponential and Logarithmic Equations
Solving Log and Exponential Equations
Inverses of Logs and Exponentials
22
(*)Standard 6 Review
(*)Summary of Notes
(*)Practice Quizzes
(*)Study Materials
Authored in PreTeXt
Chapter
3
Composition
This is the introduction to the chapter
3.1
Evaluating a Composition of Functions
3.2
Simplifying a Composition of Functions