Relations and Functions 2.1 Relations and Functions

What is a Relation? A relation is a set of pairs of inputs and outputs. They can be written as an ordered pair They can be graphed They can be expressed in a mapping diagram

Ordered Pairs 0, 1, 2, 5 are all considered “inputs” These are all the “x” coordinates 5, 7, 6, 0 are all considered “outputs” These are all the “y” coordinates

Graph

Mapping Diagram INPUT OUTPUT

Create a mapping diagram

Domain Range Set of all inputs of a relation The “x” coordinate The set of all outputs of a relation The “y” coordinate

Example Find the domain and range of the relation

Functions A function is defined as a relation in which every input (element in the domain) is paired with exactly one output (element in the range).

Mapping diagrams 1 2 4 5 7 -2 3 9 12 Every input mapped to exactly one output-this is a function.

Mapping diagrams 1 2 4 5 -2 1 3 9 12 7 7 is mapped to TWO outputs-NOT a function

Graphing The vertical line test is used when determining if a graph of a relation is a function. If we can draw a vertical line through every part of the graph and have it only go through ONE point, then the relation is a function.

Graph

Graph

Ordered Pairs When looking at ordered pairs to determine if they represent a function, there can be no repeating x’s.

Ordered Pairs-Determine if they represent a function

Function notation When using function notation, we use F(x) instead of y

How to work with function notation For each function, find f(3), f(1) and f(9)

Homework 8/29: #6 pg 42 1,2,6-21, 24-37 8/30: #7 pg 534 2-28 even, 36-40 all 8/31: QUIZ 1.3-9.7 9/1: #8 pg 59 2-44 even, 46-48 all, 50-54 even, 56 (use a table to graph)