1. Do Now Find the domain & range:

2. Answers to Homework 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

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

4. Day 6: Relations & Functions

5. 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]

6. 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 -5 -2 3 -5 0 4 8 #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

7. 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 35673567 -7 -6 -3

8. Functions What is a function? A relation where one element in the domain is paired with exactly one element in the range. DOMAIN RANGE -5 0 4 8 -5 -2 3 Not a function because 3 in the domain is paired with 0 and 8 in the range. DOMAIN RANGE -5 0 4 -4 0 3 8 Is a function because each element of the domain leads to one element in the range.

9. 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 #.

10. Functions This is not a function because when 12 is put into the machine, 12 or 5 is the output. DOMAIN RANGE -2 5 10 12 -7 10 12 DOMAIN RANGE -8 -4 0 3 8 This is a function because each element in the domain is paired to one element in range.

11. Determine if the relation is a function DOMAIN RANGE -3 1 5 10 -2 1 7 9 DOMAIN RANGE 1 14 800 -7 -4 6 11 This is a function because when every number goes into the machine, you know exactly what the output will be.

12. Determine if the relation is a function XY -25 110 71 9-3 XY -7800 -41 614 1114 The relation is a function because each input leads to exactly one output.

13. Determine if the table shows a function xy -11-31 -2-4 02 723 xy 25 48 613 215 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.

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