1. 3.1 – Functions vs. Relations

2. Relation
Any set of input that has an output

3. Function
A relation such that every single input has exactly ONE output
Each element from the domain is paired with one and only one element from the range

4. How do I know it’s a function?
Look at the input and output table – Each input must have exactly one output.
Look at the Graph – The Vertical Line test: NO vertical line can pass through two or more points on the graph

5. Real World Talk…
**Never _________________________________!!!**

6. function Example 1: {(3, 2), (4, 3), (5, 4), (6, 5)}
Function or relation?
Example 1:
{(3, 2), (4, 3), (5, 4), (6, 5)}
function

7. Function or relation?
Example 2:
Function

8. Function or relation?
Example 3:
relation

9. function Function or relation? Example 4:
( x, y) = (student’s name, shirt color)
function

10. Function or relation?
Example 5: Red Graph
relation

11. function Function or relation? Jacob Angela Nick Honda Greg Toyota
Example 6
Jacob
Angela
Nick
Greg
Tayla
Trevor
Honda
Toyota
Ford
function

12. function A person’s cell phone number versus their name.
Function or relation?
Example 7
A person’s cell phone number versus their name.
function

13. Function Notation

14. Function form of an equation
Function Notation is a way to name a function. It is pronounced “f of x”
f(x) is a fancy way of writing “y” in an equation.

15. Evaluating Functions

16. Tell me what you get when x is -2.
8. Evaluating a function
Tell me what you get when x is -2.
f(x) = 2x + 3 when x = -2
f(-2) = 2(-2) + 3
f(-2) =
f(-2) = - 1

17. Tell me what you get when x is 3.
9. Evaluating a function
Tell me what you get when x is 3.
f(x) = 32(2)x when x = 3
f(3) = 32(2)3
f(3) = 256

18. Tell me what you get when x is -3.
10. Evaluating a function
Tell me what you get when x is -3.
f(x) = x2 – 2x + 3 find f(-3)
f(-3) = (-3)2 – 2(-3) + 3
f(-3) =
f(-3) = 18

19. Tell me what you get when x is 3.
11. Evaluating a function
Tell me what you get when x is 3.
f(x) = 3x + 1 find f(3)
f(3) =
f(3) = 28

20. Function Practice Worksheet
Homework/Classwork
Function Practice
Worksheet