Functions

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)

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

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)}

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

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 = -110000 x2 + y2 = 16 y3 = 2x4 – 6x +11 x = 6

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