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=x^{3} or x=2" means the same thing as "Given f(x)=x^{3} 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**

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!