1. 4.8 Functions and Relations
Goal: Decide whether a relation is a function and use function notation

2. Definitions Relation - Any set of ordered pairs
Function -A type of relation where there is exactly one output for every input. For every x there is exactly one y.

3. x y 1 2 6 7 x y 1 2 6 7
Not a Function
Function

4. y = 2x x-y chart mapping x y input output -2 -1 1 2 -4 -2 2 4 -4 -2 -21 2 -4 -2 2 4 -4 -2 -2 -1 1 2 2 4
Function

5. Determine whether the equation is a function.x y
input
output x y
input
output -2 -1 1 2 2 1 2 1 -2 -1 1 2 -2 -2 -1 -1 1 1 1 1 2 2 2 2
Function
Not a Function

6. Vertical Line Test - Functionsy y y y x x x x
Function y y y y x x x x

7. Vertical Line Test - Functionsy y y y x x x x
Function
Function y y y y x x x x

8. Vertical Line Test - Functionsy y y y x x x x
Function
Function
Not a
Function y y y y x x x x

9. Vertical Line Test - Functionsy y y y x x x x
Function
Function
Function
Not a
Function y y y y x x x x

10. Vertical Line Test - Functionsy y y y x x x x
Function
Function
Function
Not a
Function y y y y x x x x
Not a
Function
Function
Not a
Function
Not a
Function

11. x y Tell whether the relation below is a function. input output 1) 3)1 x 5
Function
Not a
Function 2 3 2) x y 4)
input
output -3 -1 1 2 3 -2 4 -1
Not a
Function 5
Not a
Function 6

12. Function Notation

13. Evaluate the following.

14. Evaluate the function over the domain,
x = -1, x = 0, x = 2.

15. Graph the linear function.
f(x) x -3 -2 -1 1 2 3 6 5 4 3 2 1 x