1. Common Core Math 8 India Walton
Functions
Common Core Math 8
India Walton

2. Vocabulary Relation – set of ordered pairs
Function - a relationship for which there is exactly one output for each input
Mapping Diagram - diagram that matches input values with their corresponding output values using arrows
Vertical Line Test - a test used to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph of the relation in more than one point.

3. X and Y Values Given the relation: State the x-values
{(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)}
State the x-values
X: {0,1, 2, 3}
State the y-values:
Y: {-6, 0, 4}

4. Graph Equation Table of values A set of ordered pairs Mapping
A function is a relation that gives a single
output number for every valid input number
(x values cannot be repeated).
A relation is a rule that produces one or more
output numbers for every valid input number
(x and y values may be repeated).
There are many ways to represent relations:
Graph
Equation
Table of values
A set of ordered pairs
Mapping
These are all ways of showing a relationship between two variables.

5. Function
X values are always located
on the right and y values are
on the left.
They can be represented by
words, symbols or numbers.
This represents a function as every input value (x) has only been used once.

6. x y 5 6 7 Relations and functions can be shown many different ways.
Are these relations or functions?
Function
&
Relation x y 1 2 3 4
x y 5 6 7 5 6 7
(1, 5), (2, 6), (3, 7), (4, 6)

7. Are these relations or functions?
Not a Function but a
Relation x y
x y 5 6
1 7
1 6 1 2 5 6 7

8. Are these relations or functions?x y
Not a function
But a relation 5 6 8 11 1 2 3
x y 5 6 11 8

9. Table
{(3, 4), (7, 2), (0, -1),
(-2, 2), (-5, 0), (3, 3)}

10. Functions
A function is a relation in which the members of the x-values DO NOT repeat.
So, for every x-value there is only one y-value that corresponds to it.
y-values can be repeated.

11. Do the ordered pairs represent a function?
{(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}
No, 3 is repeated in the x-values.
{(4, 1), (5, 2), (8, 2), (9, 8)}
Yes, no x-coordinate is repeated.

12. A relation assigns the x’s with y’s1 2 2 4 3 6 4 8 10 5
X-values
Y-values
This relation can be written {(1,6), (2,2), (3,4), (4,8), (5,10)}

13. No x has more than one y assigned All x’s are assigned
A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B.
A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B.
A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B.
Set A: x-values 1 2 3 4 5
Set B: y-values 2 10 8 6 4
No x has more than one y assigned
All x’s are assigned
This is a function ---it meets our conditions
Must use all the x’s
The x value can only be assigned to one y

14. Let’s look at another relation and decide if it is a function.
The second condition says each x can have only one y, but it CAN be the same y as another x gets assigned to.
Set A: x-values 1 2 3 4 5
Set B : y-values 2 10 8 6 4
No x has more than one y assigned
All x’s are assigned
This is a function ---it meets our conditions
Must use all the x’s
The x value can only be assigned to one y

15. A good example that you can “relate” to is students in our maths class this semester are set A. The grade they earn out of the class is set B. Each student must be assigned a grade and can only be assigned ONE grade, but more than one student can get the same grade (we hope so---we want lots of A’s). The example shown on the previous screen had each student getting the same grade. That’s okay.
A good example that you can “relate” to is students in our maths class this semester are set A. The grade they earn out of the class is set B. Each student must be assigned a grade and can only be assigned ONE grade, but more than one student can get the same grade (we hope so---we want lots of A’s). The example show on the previous screen had each student getting the same grade. That’s okay. 1 2 2 4 3 6 4 8 10 5
2 was assigned both 4 and 10
Is the relation shown above a function? NO
Why not???

16. This is not a function---it doesn’t assign each x with a y
Check this relation out to determine if it is a function.
It is not---3 didn’t get assigned to anything
Comparing to our example, a student in maths must receive a grade
Set A: x-values 1 2 3 4 5
Set B:y-values 2 10 8 6 4
This is not a function---it doesn’t assign each x with a y
Must use all the x’s
The x value can only be assigned to one y

17. Check this relation out to determine if it is a function.
This is fine—each student gets only one grade. More than one can get an A and I don’t have to give any D’s (so all y’s don’t need to be used).
Set A: x-values 1 2 3 4 5
Set B: y-values 2 10 8 6 4
Must use all the x’s
This is a function
The x value can only be assigned to one y

18. Graphs of a Function
Vertical Line Test:
If a vertical line is passed over the graph and it intersects the graph in exactly one point, the graph represents a function.

19. Vertical Line Test: if every vertical line you can draw goes through only 1 point then the relation is a function.

20. Does the graph represent a function?x y
Yes x y

21. Does the graph represent a function?No x y x y

22. Does the graph represent a function?
Yes No x y x y

23. Which Are Functions?
(b)
(a)
(d)
(c)

24. Which Are Functions?
(a)
(b)
(c)
(d)
(a) and (c)