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MA 109 Student Guide
Contents
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Contents
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1
Preliminaries
Plotting Points and the Coordinate Plane
Intercepts
I
Functions and Function Notation
2
Function Notation
Evaluating Functions from a Formula
Piecewise Functions
Functions as Graphs and Tables
Algebra with Functions
Solving with Functions
3
Domain and Range
Interval Notation
Domain from a Graph
Range from a Graph
Domain from a Formula
4
Composition
Evaluating a Composition of Functions
Simplifying a Composition of Functions
5
Transformations
Vertical Shifts
Horizontal Shifts
Vertical Scales
Horizontal Scales
Reflections
Combining Transformations
6
Inverse Functions
Evaluating Inverse Functions
Finding a Formula for the Inverse
Domain and Range of an Inverse
II
Linear Functions
7
Linear Functions
Slope of a Line
Equation of a Line
8
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
9
Linear Models
Models with One Line
Models with Systems of Equations
10
Rate of Change
Computing Average Rate of Change
Difference Quotient
III
Polynomial and Rational Functions
11
Quadratic Functions
Roots of Quadratic Functions
Equations of Quadaratic Functions
12
Polynomial Functions
Roots of Polynomials
Equation of Polynomials
End Behavior of Polynomials
13
Rational Functions
Domain of Rational Functions
End Behavior of Rational Functions
IV
Exponential and Logarithmic Functions
14
Exponential Functions
Equations of Exponential Functions
Graphs and End Behavior of Exponential Functions
The Number
\(e\)
15
Logarithmic Functions
Evaluating Logarithmic Functions
Graphs of Logarithmic Functions
The Natural Log
16
Logarithm Properties
Combining Logarithms
Expanding Logarithms
17
Exponential and Logarithmic Equations
Solving Simple Equations
Using Log and Exponenetial Rules
(*)Solving Complicated Equations
18
Exponential Models
(*)Exponenetial Growth
(*)Exponential Decay
Authored in PreTeXt
Chapter
4
Composition
This is the introduction to the chapter
4.1
Evaluating a Composition of Functions
4.2
Simplifying a Composition of Functions