1. Functions & Relations

2. Relation
Any set of input that has an output

3. Frayer Model
Definition
Examples
Relation
Linear
Non-Linear

4. Frayer Model
Definition
Examples
Relation
Linear
Non-Linear

5. Frayer Model A set containing pairs of numbers Relation Definition
Examples
A set containing pairs of numbers
Relation
Linear
Non-Linear

6. Frayer Model {(2,1), (1,3), (0,4)} A set containing pairs of numbers 2
Definition
Examples
{(2,1), (1,3), (0,4)}
A set containing pairs of numbers 2 1 1 3 4 x y 2 1 1 3 4
Relation
Linear
Non-Linear

7. Frayer Model {(2,1), (1,3), (0,4)} A set containing pairs of numbers 2
Definition
Examples
{(2,1), (1,3), (0,4)}
A set containing pairs of numbers 2 1 1 3 4 x y 2 1 1 3 4
Relation
Linear
Non-Linear

8. Frayer Model {(2,1), (1,3), (0,4)} A set containing pairs of numbers 2
Definition
Examples
{(2,1), (1,3), (0,4)}
A set containing pairs of numbers 2 1 1 3 4 x y 2 1 1 3 4
Relation
Linear
Non-Linear

9. Domain
x – coordinates
Input
Independent variable

10. Range
y – coordinates
Output
Dependent variable

11. When listing the domain and range,
Put in order from least to greatest
Only list repeats once

12. Example
Write the domain and range for the following relation. {(2, 6), (-4,-8), (-3,6), (0,-4)}

13. You Try
1) Write the domain and range for the following relation. {(-5,2), (3,-1), (3,2), (1,7)}

14. You Try
What are the domain and range?

15. 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

16. How do we describe
FUNCTIONS ?

17. Frayer Model
Definition
Examples
a relation in which each input (x value) is paired with exactly one output (y value).
Function
Linear
Non-Linear

18. Frayer Model {(1,2), (2,4), (3,6)} 1 2 3 2 4 6 x y 1 2 3 2 4 6
Definition
Examples
{(1,2), (2,4), (3,6)}
a relation in which each input (x value) is paired with exactly one output (y value). 1 2 3 2 4 6 x y 1 2 3 2 4 6
Function
Linear
Non-Linear

19. Frayer Model {(1,2), (2,4), (3,6)} 1 2 3 2 4 6 x y 1 2 3 2 4 6
Definition
Examples
{(1,2), (2,4), (3,6)}
a relation in which each input (x value) is paired with exactly one output (y value). 1 2 3 2 4 6 x y 1 2 3 2 4 6
Function
Linear
Non-Linear

20. Frayer Model {(1,2), (2,4), (3,6)} 1 2 3 2 4 6 x y 1 2 3 2 4 6
Definition
Examples
{(1,2), (2,4), (3,6)}
a relation in which each input (x value) is paired with exactly one output (y value). 1 2 3 2 4 6 x y 1 2 3 2 4 6
Function
Linear
Non-Linear

21. Very Important!!!
All functions are relations but not all relations are functions.

22. How do I know it’s a function?
Look at the input and output table – Each input must have exactly one output. (Domains CANNOT repeat!!!)
Look at the Graph – The Vertical Line test: NO vertical line can pass through two or more points on the graph

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

24. Are these relations functions?
(1, 2), (3, 4), (1, 5), (2, 6)
(6, 9), (7, 10), (8, 11), (8, –11)
(–1, –5), (–2, –7), (0, 3), (1, –5)
4. (2, 4), (3, 5), (2, -4), (3, –5)

25. Are these relations functions?x 1 2 3 4 y 5 6 7 1. 2. 3. x 2 4 5 Y 1 3 x 6 5 4 3 Y -1 -2 -3 -4

26. Are these relations functions?1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

27. 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!

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

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

30. An Equation is not a Function if…
the “y” variable is raised to an EVEN power;
x = any number; x = 5 and x = -9 these are vertical lines.

31. Are these functions? y = x 2 x + y 4 = 5 y = x + 3 y + 6 = x 3 x = 3
Yes
No, y is raised to an even power!
No, because the line is vertical!

32. How do you know if a relation is a function?
Tell Your Neighbor
How do you know if a relation is a function?

33. Wednesday: Warm Up
Is this relation a function? Explain how you know. {(3,4), (0,7), (3, -4), (2,5)} Vocab Warm-Up Page 465

34. Tuesday Warm Up

35. Thursday Warm-Up
Create a table with two columns labeled “Relation and Function” and “Relation Only”
Give examples of each in the following forms:
ordered pairs
table
mapping
graph

36. Test Your Neighbor
Make a list of coordinate pairs. Ask your neighbor if the relation is a function.

37. Error Analysis-Functions
Success Starter for 1/9/17
Error Analysis-Functions
When asked whether the relation {(-4,16), (-2,4), (0,0), (2,4)} is a function, Zion stated that the relation is not a function because 4 appears twice. What error did Zion make? How would you explain to the student why this relation is a function? Also, write the domain and range.

39. Lesson Review
Write the definition of the following vocabulary terms: Domain Range Relation Function

40. Make a mapping diagram of a relation
Make a mapping diagram of a relation. Ask your neighbor if the relation is a function.

41. Does the graph represent y as a function of x? Explain.

43. Warm Up