Types of functions:

Linear

bmxy

Quadratic

cbxaxy 2

Absolute Value

xy

Exponential xbay )(

Constant

by

Polynomial

Step

Trigonometric

Logarithmic

Square Root Functions

Rational Functions

Vocabulary•Relation – a set of ordered pairs Example – {(-1,1), (2,3), (2,1), (2,-1),

(5,1)}

 

 

•Function – a relation for which each x corresponds to exactly one y

Use the vertical line test to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph at more than one point.  

Vertical Line Test

This graph is a function since there are no vertical lines that hit the graph more than once.

 

Ways of showing functions:

• Graphically- use vertical line test!

 

Ways of showing functions:

• Equations - use your calculator to see the graph

262 2 xxxf

 

•Tables (functions have no repeated x’s) Ex of function ex of non-function

x y

-3 9

-3 4

-1 1

0 0

1 1

2 4

3 9

x y

-3 9

-2 4

-1 1

0 0

1 1

2 4

3 9

 

• Mappings – look to see if every element of the first set has ONLY ONE element it matches in the second set.

 

Set notation (set builder and interval notation) • Set builder notation: The set {x : x > 0} is read aloud, "the set of all x such that x is greater than 0." The set {x: x ≠ 3} is the set of all real numbers except 3

The set {x | -2 < x < 5} is the set of numbers such that values of x are greater than negative 2 and less than 5.

 

• Interval notation:

A notation for representing an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included. For example, [3, 8) is the interval of real numbers between 3 and 8, including 3 and excluding 8.

Another example: The interval: which includes -1 and excludes 2.