Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Elementary Algebra
Topic: Functions and Graphs I
Subtopic: Functions I - Introduction

Overview

Today we introduce the concepts of functions and relations. Relations will be given in the form of sets of ordered pairs, mappings, graphs, or equations. Try to seem these as just different ways to visualize/communicate the same information.

This is a vital section since the remainder of this course and intermediate algebra deal with different types of functions and their graphs. There is lots of important terminology here. Be sure you well versed in recognizing functions given a set of ordered pairs (e.g., why is {(0,1),(0,2),(1,3),(2,3)} not a function?), a mapping, a graph (using the VLT), or an equation (which you can just graph and determine visually).

A key thing to remember is that if a relation has "same x different y" then it is NOT a function.

Notation Caution: f(x) ... that is "f of x" ... does not mean f times x! It does mean the equation is a function called f and the input variable is x. You can think of "f(x)" as meaning "y". In other words, "Evaluate y=x3 or x=2" means the same thing as "Given f(x)=x3 find f(2)".

Objectives

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

• 3.3.1 Determine if a relation is a function or not given: set of ordered pairs, mapping, graph, or equation
• 3.3.2 Use the vertical line test to determine if a curve is a graph of a function or not
• 3.3.3 Understand function notation and use/write it properly
• 3.3.4 Evaluate functions algebraically for given values of the input variable
• 3.3.5 Evaluate functions by observation of its graph

Terminology

Terms you should be able to define: set, mapping, relation, function, vertical line test (VLT)

Text Notes
This section contains lots of important new terminology, notation, and processes. Plan to spend significant time studying it!

rev. 2021-03-31