1. Southaven Middle School 8th Math Case 21 Review
Functions 8.F
Southaven Middle School th Math Case 21 Review

2. This is going to be our first experience with something that's a little more like a concept...
But, it's really not that bad.  We'll just do a little at a time!
You can think of a function as being a box with a special rule... stuff goes in the box... and stuff comes out of the box.
Let's start with a movie title box:
THE RULE:  Spit out the first letter of the movie title.                             (Only movie titles can go in.)

3. What if we tried this?
Hmm Dalmations starts with a number, not a letter...  So, we can't even put it in the box!
(Think about it...  Where would they have this movie at the video store?  Before the A's!)
Here are some official math terms:
The stuff that goes IN the box (the INPUT) is called the DOMAIN.
The stuff that spits OUT of the box (the OUTPUT) is called the RANGE.

4. Domain: In a set of ordered pairs, (x, y), the domain is the set of all x-coordinates.
Range: In a set of ordered pairs, (x, y), the range is the set of all y-coordinates.

5. Functions
Function of x – a relation in which no two ordered pairs have the same x-value
Examples:
(5, 5) and (5, 2) not a function
(3, 5) and (5, 2) function
(13, -24) and (13, 76) not a function
(1, 24) and (7, 24) function

6. 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

7. 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

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

9. The Vertical Line Test (also know as the “pencil test”)
Not every equation is a function.  Remember, for an equation to be a function each number x in the domain must produce exactly one number y in the range.  Graphically this means that the graph of a function cannot contain two points with the same x-coordinate and two or more different y-coordinates.  The Vertical Line Test was created, to identify functions by examining their graphs.
The Vertical Line Test (also know as the “pencil test”)
A set of points in the Cartesian Coordinate System is the graph of a function if and only if every vertical line intersects with the graph in at most one point.

10. 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!

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

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

13. Is this a graph of a function?
(-3,3)
(4,4)
(1,1)
(1,-2)

14. Now Lets Practice Identifying Functions
Determine whether {(–5, 2), (–2, 5), (0, 7), (0, 9)} is a function. Explain.
Answer: This relation is not a function because the element 0 in the domain is paired with both 7 and 9 in the range.
Example 6-1c

15. Practice Identifying Functions
Determine whether each relation is a function. Explain. a.
Answer: This mapping represents a function since, for each element of the domain, there is only one corresponding element in the range.
Example 6-1d

16. Practice Identifying Functionsb.
c. {(3, 0), (1, 2), (4, 0), (5, –1)} –1 3 –4 2 –2 1 Y X
Answer: This relation is not a function because the element 3 in the domain is paired with both 2 and –1 in the range.
Answer: This is a function because the mapping shows each element of the domain paired with exactly one member of the range.
Example 6-1d

17. Closure IS there a difference between a relation and a function?
With your partner discuss the difference if any.
Class discussion about difference that partners concluded.
List the ways to determine if a relation is a function.