1. Relations and Functions
2.1
Relations and Functions

2. 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

3. 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

4. Graph

5. Mapping Diagram
INPUT
OUTPUT

6. Create a mapping diagram

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

8. Example
Find the domain and range of the relation

9. 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).

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

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

12. 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.

13. Graph

14. Graph

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

16. Ordered Pairs-Determine if they represent a function

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

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

19. Homework
8/29: #6 pg 42 1,2,6-21, 24-37
8/30: #7 pg even, all
8/31: QUIZ
9/1: #8 pg even, all, even, 56 (use a table to graph)