FunctionsRelation such that each element x in a set A maps to EXACTLY ONE element y in a set B Set A: Domain = set of all numbers for which

the formula makes sense and defines real numbers (x values) x = independent variable

Set B: Range = f(x) = set of all possible f(x) as x varies through the domain (y values) y = dependent variable

Example Find the domain of . [Think: What can’t happen?] You can’t have zero on the bottom of a

fraction.

Domain You may just write:  

Example Find the domain of .

−+¿

−Domain

Vertical Line Test A curve in the xy-plane is the graph of a

function of x if and only if NO vertical line intersects the curve more than once

If any vertical line hits more than one point, the graph is not a function

Example Determine if each is a function.

Yes No

Homework: p. 14 #1, 3, 11, 15, 29

Even v. Odd Functions

Even – symmetric with respect to y – axis

(equal y values)

Odd – symmetric with respect to origin

(opposite y values)

Function Guide

1. Constant Ex:

Even2. Identity

Odd

3. Absolute Value Ex: Even

4. Square Root Ex: Neither

X Y

0 0

1 1

2 1.4

3 1.7

4 2

X Y

-2 2

-1 1

0 0

1 1

2 2

5. Quadratic Ex: Even

6. Cubic Ex: Odd

X Y

-2 4

-1 1

0 0

1 1

2 4

X Y

-2 -8

-1 -1

0 0

1 1

2 8

Composition of Functions

Ex:

In this case,

𝑓 (𝑥−3)¿ (𝑥−3)2=𝑥2−6 𝑥+9𝑔 (𝑥2) ¿ 𝑥2−3

Piecewise Defined Functions

Greatest Integer Function

greatest integer

D = all real #’s R = all Z

X Y

0 0

0.5 0

0.9 0

1 1

“Step Function”

Examples

Homework: p. 14 #9, 31, 41-47 odd

Graph and Turn In for 20 Points