Do Now Find the domain & range:

Answers to Homework

Homework Need help? Look in section 2.1 – Relations & Functions in your textbook Worksheet: Functions WS

Day 6: Relations & Functions

Relations What is a relation? A set of pairs of x – values and y – values State the relation Relation: (-5, 4), (-2, -5), (3, 0), (3, 8) State the domain of the relation in interval notation Domain: [-5]  [-2]  [3] State the range of the relation in interval notation Range: [-5]  [0]  [4]  [8]

Relations Describing relations using a mapping diagram Relation: (-5, 4), (-2, -5), (3, 0), (3, 8) Domain: [-5]  [-2]  [3] Range: [-5]  [0]  [4]  [8] DOMAIN RANGE #1: Create a column for domain and one for range #2: Add domain and range values #3: Draw arrows to show how each element in the domain pairs up with the elements in the range. HOW TO CREATE A MAPPING DIAGRAM

Relations Given the relation below, state the domain and range and create a mapping diagram. Relation: (6,-6), (7,-7), (3,-3), (5,-7) Domain: [3]  [5]  [6]  [7] Range: [-7]  [-6]  [-3] DOMAIN RANGE

Functions What is a function? A relation where one element in the domain is paired with exactly one element in the range. DOMAIN RANGE Not a function because 3 in the domain is paired with 0 and 8 in the range. DOMAIN RANGE Is a function because each element of the domain leads to one element in the range.

Functions …another way to think about functions… Function as a machine where a number goes in and are manipulated (add, subtract, etc.) to turn into something else. Numbers that go in are the domain (x – values). Numbers that come out are the range (y – values). Every time you put a # into the machine, the machine has to output only one #.

Functions This is not a function because when 12 is put into the machine, 12 or 5 is the output. DOMAIN RANGE DOMAIN RANGE This is a function because each element in the domain is paired to one element in range.

Determine if the relation is a function DOMAIN RANGE DOMAIN RANGE This is a function because when every number goes into the machine, you know exactly what the output will be.

Determine if the relation is a function XY XY The relation is a function because each input leads to exactly one output.

Determine if the table shows a function xy xy The relation is a function because each input leads to exactly one output. The relation is not a function because 2 leads to outputs 5 and 15.

Did you meet today’s objective? What is a relation? What makes a relation a function?