1. Functions

2. Key Terms and Definitions
Relation: A set of ordered pairs (or input and output values)
Domain: set of input values (usable “x” values)
Listed least to greatest (left to right)
Range: set of output values (usable “y” values)
Listed least to greatest (lowest to highest)

3. How to tell if a Relation is a Function
Four Ways:
Presented as a set of ordered pairs
Presented as a diagram
Presented as an equation
Presented as a graph

4. How to tell if a Relation is a Function
Presented as a set of ordered pairs
Make sure no “x” values apply to two different “y” values (no repeat “x”s).
Example of a relation that IS a function:
{(1,3), (2, 5), (3,7), (4,9)}
Example of a relation that IS NOT a function:
{(1,3), (2, 5), (1,7), (4,9)}

5. How to tell if a Relation is a Function
Four Ways:
2. Presented as a diagram
Make sure “x” value is not branching out to two or more “y” values.
Function Not a Function 1 2 3 A B C 1 2 3 A B C

6. How to tell if a Relation is a Function
Four Ways:
3. Presented as an equation
Make sure equation contains “y” to the first power.
Function
Not a function
y = 2x + 3
y = 3
4x + 5y = 12
3x – 2y =
x2 + y2 = 16
y3 = 2x4 – 6x +11
x = 6

7. How to tell if a Relation is a Function
4. Presented as a graph
Make sure graph passes the “vertical line test.“
No vertical line will touch a function twice.
See chalkboard for examples