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. One input gives 2 outputs
Vocab
Function = A set of ordered pairs that has each input (x) giving exactly one output (y)
Ex: Function or not?
In a function, one input can’t give 2 different outputs! X Y -2 3 4 8 32 7 5 X Y 5 3 4 8 32 -6 X Y -2 3 -1 8 7
Yes
No;
One input gives 2 outputs
Yes

4. More Vocab (x, y) = (input, output)
f(x) is another way to write an output
Domain = the set of all inputs (x)
Range = the set of all outputs (y)
Ex: For the function f(x) = x – 3 , evaluate the following:
f(-3)
f(x+1)

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

7. 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

8. 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

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

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

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

12. 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

13. 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

14. 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

15. Function Notation

16. Evaluate the following.

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

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

19. Discrete vs. Continuous
Discrete relation: A relation where the domain is a set of individual points
Continuous relation: A relation that can be graphed with a line or smooth curve