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Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
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Course: Algebra I / 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:

Terminology

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!