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: College Algebra
Topic: Functions and Graphs
Subtopic: Library of Functions

Overview

In this lesson we study a collection of common functions, their graphs, and important features of the graphs. Most of these functions you already know well, e.g., the absolute value functions. Others may be new to you, e.g. the greatest integer function.

Objectives

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

• 2.2.1 Recognize common functions and their graphs including constant function, identity function, linear function, absolute value function, square root function, quadratic function, cubic function
• 2.2.2 Recognize special functions and their graphs including the greatest integer function and other step functions, piecewise functions, and power functions (both even power and odd power functions)
• 2.2.3 Describe features of common and special functions including domain, range, increasing, decreasing, odd, even

Terminology

Terms you should be able to define: greatest integer function, step function, piecewise function, even power function, odd power function

Mini-Lectures and Examples

Supplementary Resources

It may be helpful to have downloaded or printed a PDF of the most common functions and their graphs. Lots are available on the internet if you search on "Library of Functions". One fairly straight-forward sheet containing all the basic functions is at Library of Functions, Prof. Ann Cary, Portland CC.

rev. 2020-10-10