1. Do Now: Make a K-W-L Chart Complete what you KNOW about functions

2. Functions October 17, 2017 Can I determine if a relationship is a function?

3. A function is a relation in which each input has exactly one output.
Functions
A function is a relation in which each input has exactly one output.
f(x) y x

4. Function Notation
Input
Name of Function
Output

5. Variables Variable x is called independent variable
Variable y is called dependent variable
We use f(x) instead of y.

6. What is the domain and range?
The domain of a function is the set x. That is a collection of all possible inputs.
The range of a function is the set of all possible outputs.

7. Function Rule An algebraic expression that defines a function
For example:
What is the function’s rule?

8. Five Representations of Functions
Ordered Pairs
Mapping
Tables
Graphs
Equations

9. Tables – For each input, there is exactly one output

10. Turn and Talk
Is this a function. WHY OR WHY NOT?

11. Determine whether each relation is a function.
1. {(2, 3), (3, 0), (5, 2), (4, 3)}
YES, every domain is different!
f(x) 2 3
f(x) 3
f(x) 5 2
f(x) 4 3

12. Determine whether the relation is a function.
2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}
f(x) 4 1
f(x) 5 2
NO, 5 is paired with 2 numbers!
f(x) 5 3
f(x) 6
f(x) 1 9

13. Is this relation a function? {(1,3), (2,3), (3,3)}
Yes No
Answer Now

14. Vertical Line Test (pencil test)
If any vertical line passes through more than one point of the graph, then that relation is not a function. Are these functions?
FUNCTION!
FUNCTION!
NOPE!

15. Vertical Line Test
FUNCTION!
NO!
NO WAY!
FUNCTION!

16. Is this a graph of a function?
Yes No
Answer Now

17. Mapping Functions

18. Are these functions
YES NO

19. Carousel Start at any point in the carousel.
Move clockwise around the room.
Complete the following table:
Is the relation a function?
WHY or WHY NOT
State the domain and range of each.