1. Bell Ringer {-5 < x < 5} Except x =0 {-5 < y < 5} Domain:
Range:
State the domain and range of the relation shown ow.
{-5 < x < 5} Except x =0
{-5 < y < 5}

2. Bell Ringer Part 2 {(9,0), (-3,7),(-5,7), (-2,-10), (4,5)}
Domain: _____________________
Range: ______________________

3. How does the domain and range change?

4. Domain and Range Quick Check! (10 points)

5. LEQ: What characteristics are needed for a relation to be a function??

6. “each x goes to one and only one y”
What is a function?
Function – A relation, whereby each input value is mapped/related to one and only one output value. In other words, for each input value, there is exactly one output value.
“each x goes to one and only one y”

7. The x-value of 3 is assigned to both 6 and 5 as y-values!
What is a function?
Function : “each x goes to one and only one y”
Is this relation a function? x y 6 -2 3 13 5
No!
The x-value of 3 is assigned to both 6 and 5 as y-values!

8. The x-value of ¾ is assigned to both 3 and 5 as y-values!
What is a function?
Function : “each x goes to one and only one y”
Is this relation a function?
No!
The x-value of ¾ is assigned to both 3 and 5 as y-values!

9. To be a function, no x-values can repeat!
What is a function?
To be a function, no x-values can repeat!
Function : “each x goes to one and only one y”
Is this relation a function?
{(5,2), (3,-6), (4,1), (5,0), (5,3)}
No!
The x-value of 5 is assigned to 2, 0 and 3 as y-values!

10. Let’s look at a real world example of this…
To be a function, no
x-values can repeat!
Let’s look at a real world example of this…

11. Egg to Basket Relation 1 Egg# Basket # Egg 1 2 Egg 2 3 Egg 3 4 Egg 4 1
This relation relates numbered eggs to a numbered basket.
Play out the following relation in real-life. (That is, physically place egg #1 in basket #2, egg #4 in basket #1 and so on…)
Was this physically possible?
Is this a function
(aka – do any “x”-values repeat?)
Egg#
Basket #
Egg 1 2
Egg 2 3
Egg 3 4
Egg 4 1
Yes!
Yes! It’s a function.

12. Egg to Basket Relation 3 Egg# Basket # Egg 1 3 Egg 2 Egg 3 1 Egg 4 4
This relation relates numbered eggs to a numbered basket.
Play out the following relation in real-life. (That is, physically place egg #1 in basket #2, egg #4 in basket #1 and so on…)
Was this physically possible?
Is this a function
(aka – do any “x”-values repeat?)
Egg#
Basket #
Egg 1 3
Egg 2
Egg 3 1
Egg 4 4
So it was ok to have more than one of the same
y-value?
Yes!
Yes!
Yes! It’s a function.

13. No, egg 2 can’t be placed in baskets 3 and 4 at the same time!
Egg to Basket Relation 2
This relation relates numbered eggs to a numbered basket.
Play out the following relation in real-life. (That is, physically place egg #1 in basket #2, egg #4 in basket #1 and so on…)
Was this physically possible?
Is this a function
(aka – do any “x”-values repeat?)
Egg#
Basket #
Egg 1 1
Egg 2 3 4
Egg 3 2
No, egg 2 can’t be placed in baskets 3 and 4 at the same time!
NOOOOO!!!

14. Try again… is this relation a function?
#1 on note sheet! x y 4 5 7 6 1 2 -9 3
Yes!
(no x-values repeat)
Does it matter that I have two zeros for y?
Nope!

15. Try again… is this relation a function?
#2 on note sheet! x y 4 5 7 6 1 2 -9
No!
(6 repeats as an x-value)

16. Try again… is this relation a function?
{(4,2), (3,-7), (5,6), (-5,2), (-3,3)}
Yes!
(no x-values repeat)

17. Try again… is this relation a function?
#3 on note sheet!
{(4,2), (-5,-7), (5,6), (-5,2), (-3,3)}
No!
(-5 repeats as an x-value)

18. Try again… is this relation a function?
#4 on note sheet!
No!
(3 repeats as an x-value, it is mapped to both b and c)

19. Try again… is this relation a function?
Yes!
(no x-values are mapped twice)
Egg 2 and Egg 3 can physically both be placed in basket C.

20. Stop here day 1?

21. Bell Ringer {2,5,7,9,11,13} yes {1,2,3,4,5,6} Domain: Range:
State the domain and range of the relation and determine if it is a relation.
Domain:
Range:
Function? (yes or no)
{1,2,3,4,5,6}
{2,5,7,9,11,13}
yes

22. LEQ: What characteristics are needed for a relation to be a function??

23. Relations in the Form of Graphs Is it a function?
#5 on note sheet!
PROBLEM!
PROBLEM!
PROBLEM!
No!
(many values repeat as x-values)
(8,6)
(-2,2)
(3,4)
(-2,-2)
(8,-6)
(3,-4)

24. Relations in the Form of Graphs Is it a function?
Do you remember from your internet research what trick we could use to test if a graph is a function?
Vertical Line Test!

25. Relations in the Form of Graphs Is it a function?
Vertical Line Test!
The Vertical Line Test tells me that if I can draw a vertical line ANY WHERE on my graph and it touches the graph in more than one place, the relation is NOT a function.

26. Relations in the Form of Graphs Is it a function?
Yes!
(passes vertical line test)

27. Relations in the Form of Graphs Is it a function?
PROBLEM!
NO!
(fails vertical line test)

28. Relations in the Form of Graphs Is it a function?
#6 on note sheet!
How about now?
Yes!
(passes vertical line test)

29. Relations in the Form of Graphs Is it a function?
PROBLEM!
PROBLEM!
NO!
(fails vertical line test)

30. Relations in the Form of Graphs Is it a function?
#7 on note sheet!
Yes!
(passes vertical line test)

31. Relations in the Form of Graphs Is it a function?
Yes!
(passes vertical line test)

32. Relations in the Form of Graphs Is it a function?
#8 on note sheet!
Yes!
(passes vertical line test)

33. Relations in the Form of Graphs Is it a function?
#9 on note sheet!
Yes!
(passes vertical line test)

34. Relations in the Form of Graphs Is it a function?
Yes!
(passes vertical line test)

35. Relations in the Form of Graphs Is it a function?
#10 on note sheet!
PROBLEM!
PROBLEM!
PROBLEM!
NO!
(fails vertical line test)

36. Relations in the Form of Graphs Is it a function?
Yes!
(passes vertical line test)

37. Relations in the Form of Graphs Is it a function?
#11 on note sheet!
Yes!
(passes vertical line test)

38. Relations in the Form of Graphs Is it a function?
#12 on note sheet!
How about now?
PROBLEM!
NO!
(fails vertical line test)

39. Relations in the Form of Graphs Is it a function?
PROBLEM!
No!
(fails vertical line test)

40. Team Huddle
Get out your Domain and Range Notes 1, 2 and 3 from last week. Go through each example on the note sheet and circle the graph IF IT IS A FUNCTION. Do not circle it if it is not a function.

41. Summarizer… Create a relation Exchange with a partner
Decide if you partner’s relation is a function
Exchange papers and check each other’s work