1. A relation pairs input values with output values. The set of input values (the independent variable) is called the domain. The set of output values (the dependent variable) is called the range. A relation is a function if there is exactly one output for each input. It is NOT a function if any input has more than one output Relations

2. Identify the Domain and Range. Then tell if the relation is a function. InputOutput -3 3 1 1 3 -2 4 Function? Yes: each input is mapped onto exactly one output Domain = {-3, 1,3,4} Range = {3,1,-2}

3. Identify the Domain and Range. Then tell if the relation is a function. InputOutput -3 3 1 -2 4 1 4 Domain = {-3, 1,4} Range = {3,-2,1,4} Function? No: input 1 is mapped onto Both -2 & 1

4. InputOutput -3 3 1 1 4 -2 4 (4,4) (-3,3) (1,1) (1,-2)

5. Vertical Line Test Slide any vertical line (pencil) across the graph to see if any two points lie on the same vertical line. If there are not two points on the same vertical line then the relation is a function. If there are two points on the same vertical line then the relation is NOT a function

6. Use the vertical line test to visually check if the relation is a function. (4,4) (-3,3) (1,1) (1,-2) Function? No, Two points are on The same vertical line.

7. Use the vertical line test to visually check if the relation is a function. Function? Yes, no two points are on the same vertical line

8. Function Notation If f(x) = 5x – 2, find f(-3) f(-3) = 5(-3) – 2 = -15 – 2 = -17 As an ordered pair, the solution would be written (-3, -17) f(x) is another name for y