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Algebra I / Elem. Algebra

The Basics

1.1 Intro to Algebra
1.2 Real Number System and Calculators

Linear Equations and Inequalities

Functions and Graphs I

3.1^s Introduction to Graphing
3.2 Solving Equations Graphically
3.3 Functions I - Introduction
3.4 Functions II - Domain, Range, & Operations

Lines and thier Graphs

4.1 Intercept Points
4.2^s Slopes
4.3 Equations of Lines
4.4 Graphing Linear Inequalities

Algebra II / E&I Algebra

Linear Systems

5.1 2x2 Systems of Equations I - Graphically
5.2 2x2 Systems of Equations II - Substitution Method
5.3 2x2 Systems of Equations III - Elimination Method
5.4^s 3x3 Systems of Equations
5.5 Applications
5.6 Systems of Linear Inequalities

Exponents & Polynomials

Intermediate Algebra starts here!

Factoring

Rational Expressions

Rational Equations and Applications

Algebra III / Inter. Algebra

Radical Expressions

10.1 Roots & Radicals
10.2 Fractional Exponents
10.3 Operations I - Simplify & Multiply
10.4 Operations II - Add, Subtract, & Divide
10.5 Operations III - Distribute, Foil, & Factor
10.6^s Complex Numbers

Nonlinear Equations and Applications

11.1 Radical Equations
11.2 Quadratic Equations I - Root Method
11.3^s Quadratic Equations II - Complete the Square
11.4^s Quadratic Equations III - Quadratic Formula
11.5^s Applications - Geometry & Pythagorean Theorem

Functions and Graphs II

12.1 Parabolas I - Algebraic Approach
12.2 Pareabolas II - Graphical Approach
12.3^s Functions III - Composite & Inverse

Exponential and Logarithmic Functions

13.1^s Exponential Functions & Graphs
13.2 Logarithmic Functions & Graphs
13.3 Exponential & Logarithmic Equations

Liberal Arts Maths

Under Construction

College Algebra

Equations and Inequalitites

Functions and Graphs

Polynomial and Rational Functions

3.1 Polynomial Functions I - Introduction, Zeros
3.2 Polynomial Functions II - Division, Remainder Thm, Factor Thm
3.3 Polynomial Functions III - Complex Zeros, Fundamental Thm of Algebra, Descartes Rule
3.4 Rational Functions & Graphs
3.5 Partial Fractions

Exponential and Logarithmic Functions

Systems and Matrices

Conic Sections

Sequences and Series

7.1^s Introduction to Sequences and Series
7.2 Arithmetic Sequences and Series
7.3 Geometric Sequences and Series

Trigonometry

The Six Trigonometric Functions

Right Triangle Trigonometry

Circular Functions

Graphs of Trigonometric Functions

4.1^s Basic Graphs
4.2^s Amplitude & Period
4.3^s Vertical Translations & Phase Shift
4.4 General Equation & Graph to Equation
4.5^s Combination Graphs & Harmonic Motion
4.6^s Inverse Trigonometric Functions

Trigonometric Identities

5.1 Proving Trig Identities
5.2 Sum/Difference Identities
5.3 Double-Angle Identities
5.4^s Half-Angle Identities
5.5 IDs Involving Inverse Trig Functions

Trigonometric Equations

Oblique Triangles and the Laws

Vectors

Complex, Parametric, and Polar Forms

9.1 Trigonometric Form of Complex Numbers
9.2 Products and Quotients in Trig Form
9.3 Powers and Roots in Trig Form
9.4 Parametric Equations and Graphs
9.5^s Polar Equations and Graphs

Calculus I

Limits and Continuity

Derivatives

2.1 Definition of Derivative
2.2 Derivatives of Basic Functions
2.3 Motion and the Derivative
2.4 Product Rule, Quotient Rules, & Deriv. of Trig Functions
2.5 Chain Rule
2.6 Implicit Differentiation
2.7 Derivatives of Exponential and Logarithmic Functions
2.8 Logarithmic Differentiation
2.9^s Derivatives of Inverse Functions
2.10^s Derivatives of Inverse Trig Functions
2.11 Related Rate Applications

Analysis of Curves

3.1 Extreme Values
3.2 Mean Value Theorem for Derivatives
3.3 First Derivative Test & Increasing-Decreasing Functions
3.4 Second Derivative Test & Concavity
3.5^s Curve Sketching
3.6 Fun with Reform Calculus
3.7 Optimization Applications

Antiderivatives

Calculus II

Transcendental Functions

5.0^s Review of Transcendental Functions and thier Derivatives
5.1 Integrals Resulting in Logarithmic Functions
5.2 Integrals Resulting in Inverse Trig Functions
5.3 Hyperbolic Trigonometric Functions
5.4 Numeric and Electronic Integration

Geometry

Physics

Integration Techniques

Calculus of Infinity

Parametric, Polar, and Conic Curves

Calculus III

Under Construction

S = contains supplemental resources

Course: Algebra I / Elementary Algebra
Topic: Functions and Graphs I
Subtopic: Introduction to Graphing

Overview

Mathematics can be represented algebraically (with variables and equations as we have been doing), numerically (with tables of data), or graphically. It is this latter method on which we concentrate today. Concentrate on the graphing related terminology, then plotting points, then graphing lines by making a plug-n-chug chart. By the end of this course you will be expert graphers analyzing mathematical applications by hand as well as by using a graphing calculator or related electronic graphing device. The next few sections of material are visually inspiring which is a pretty cool way to learn algebra!

Objectives

By the end of this topic you should know and be prepared to be tested on:

3.1.1 Signs of the x and y-coordinates of points in each of the four quadrants
3.1.2 Analyze graphs that represent real-life data by being able to answer questions about a real-life situation by "reading" a given graph of the data
3.1.3 Given the graph of a line find a point that lies upon it including its x and y-intercept points
3.1.4 Given a set of points or chart of data points, plot the points and connect to form a line
3.1.5 Graph a line by the plug-n-chug method (a.k.a. point-plotting method), i.e., given a linear equation, form a chart of points that
3.1.6 Recognize that real-life data that grows (or falls) in a constant manner can be modeled by a linear equation

Terminology

Define: axes, quadrants, origin, points, coordinates, axis-intercept points, plug-n-chug (a.k.a. point-plotting)

Text Notes
Text: Intro & Inter Algebra for CS 3ed by Blitzer, sect. 3.1

This section begins with important terminology of graphs and graphing. It then covers plotting points and checking if a point is a solution to an equation, i.e. if the point lies on the graph of the equation.
Starting at the bottom of page 201 the text covers graphing an equation by the plug-n-chug chart method. The charts of data points introduced in example 5 are often called plug-n-chug charts since you are plugging in x-values and chugging out y-values (or visa versa). This text calls the plug-n-chug method of graphing "point-plotting"; either way it means to generate a table of points, plot them, and connect to form the line. This method is useful for graphing any equation not just lines!
Example 8 is an interesting read but IMO too advanced for this level class. You will not be tested on this level of mathematical modeling.

Supplementary Resources

You will need access to a (free) online grapher, graphing software for your computer, or a handheld graphing calculator for the remainder of this class. These MathOL FAQs contain helpful info:

Prof. Keely's Lesson Notes for Mathematics Online