1. 8-1: Relations and Functions

2. Definitions: Relation: a set of ordered pairs
Domain: The first coordinates (usually the x)
Range: The second coordinates (usually the y)

3. Function:
A relation where each member of the domain is paired with exactly one member of the range.
Is the graphing story we used at the start a function? How do you know?
Is the function from the Function Machine game a function? How do you know?

4. How can we systematically determine if a relation is a function?
Use a Table
Vertical Line Test

5. Use a Table Is this relation a function?
{(0, 1), (1, 2), (1, 3), (2, 4)}
Steps:
List domain values and range values in order.
Draw arrows from domain values to range values.
Each domain value can only have ONE range value if the relation is a function.

6. GRAPH & VERTICAL LINE TEST
FUNCTION?
TABLE
ORDERED PAIRS
{(0, 1), (1, 2), (1, 3), (2, 4)} 
GRAPH & VERTICAL LINE TEST

7. Vertical Line Test Is this relation a function?
{(0, 1), (1, 2), (1, 3), (2, 4)}
Steps:
Graph the ordered pairs
If a vertical line drawn on the graph would go through two points, the relation is not a function.

8. GRAPH & VERTICAL LINE TEST
FUNCTION?
TABLE
ORDERED PAIRS
{(0, 1), (1, 2), (1, 3), (2, 4)} 
GRAPH & VERTICAL LINE TEST

9. Relation Representation Practice 1
FUNCTION?
TABLE
ORDERED PAIRS
{(-2, 3), (2, 2), (2, -2)} 
GRAPH & VERTICAL LINE TEST

10. Relation Representation Practice 2
FUNCTION?
TABLE
ORDERED PAIRS
{(-5, 4), (0, -4), (5, -4)} 
GRAPH & VERTICAL LINE TEST

11. Relation Representation Practice 3
FUNCTION?
TABLE
ORDERED PAIRS
Domain Range  
GRAPH & VERTICAL LINE TEST