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MachaMath.com
MachaMath.com

Functions and Graphs

Rational and Negative Exponents

Interval Notation

Function Vocabulary

Evaluating a Function

Graphing Basics

Vertical Line Test

Domain and Range

Maxima and Minima

Tests for Symmetries

Even and Odd Functions

Piecewise Functions and Continuity

Slope of a Line

Point-Slope and Slope-Intercept Forms

Horizontal and Vertical Lines

General Form of a Line

Difference Quotient of x^2

Difference Quotient of 1/x

Difference Quotient of sqrt(x)

Shapes of Basic Functions

Transformations of Functions

Graphing a Transformed Function

Function Arithmetic

Function Composition

Even-Odd Rules for Combining Functions

1-to-1 Functions

Inverse Function Definition

Finding Inverse Functions Examples

Finding Inverse Functions More Examples

Verifying Inverse Functions

Graphing Inverse Functions

Pseudo-Inverse Functions

Functions and Graphs Exam Review

Functions and Graphs Exam Solutions

Solving Equations

Polynomial Vocabulary

How to Factor a Quadratic Polynomial

Difference of Squares

Square Root Principle

Completing the Square

Deriving the Quadratic Formula

Using the Quadratic Formula

The Discriminant

Solving a Quadratic Equation Ex 1

Solving a Quadratic Equation Ex 2

Solving an Easy Quartic Equation

Solving using Factoring by Grouping Ex 1

Solving using Factoring by Grouping Ex 2

Solving a Radical Equation Ex 1

Solving a Radical Equation Ex 2

Solving a Rational Exponent Equation Ex 1

Solving a Rational Exponent Equation Ex 2

Solving an Equation Quadratic in Form Ex 1

Solving an Equation Quadratic in Form Ex 2

Solving an Equation Quadratic in Form Ex 3

Solving an Absolute Value Equation Ex 1

Solving an Absolute Value Equation Ex 2

Polynomial and Rational Functions

Vertex Form of a Quadratic Function

Graphing a Parabola

Optimization Problem (Quadratic) Example

Secret Trick to Find Vertex of a Parabola

Polynomial Curves End Behavior

Multiplicities of Zeros

Polynomial Curve Turning Points

Graphing a Polynomial Function

Polynomial Long Division

Synthetic Division

Synthetic Substitution

Remainder Theorem

Factor Theorem

Corollary to the FTC Proof

Rational Root Theorem

Descartes's Rule of Signs

Factoring with the RRT and DRoS

Graphing Rational Functions

Rational Function with Oblique Asymptote

Rational Function Larger Degree Numerator

Exponential and Logarithmic Functions

Exponential Functions and Graphs

Compound Interest Find Maturity Value

Select Between Investment Options

Euler's Number, e

Logarithms as Inverses of Exponents

Logarithm Change of Bases Formula

Evaluating Logarithms Two Ways

Graphing Logarithms (Domain and Range)

Time to Double an Investment

Interest Rate to Triple Investment

Expanding and Condensing Logarithms

Solving Logarithmic Equations

Exponential and Logarithmic Equations

Solving Systems of Two Linear Equations

Systems of Equations

Gaussian Elimination, Augmented Matrices

4x4 System Example

Inconsistent and Dependent Systems

© Drew Thomas Macha, Ph.D.

dtmacha-at-mnu-dot-edu