1. Functions
&
Relations

2. {(-3,1), (0,-2), (3,−2)} Relation- a set of ordered pairs
Ex: {(-3,1), (0,-2), (3,−2)}
Relations can be expressed 3 ways:
{(-3,1), (0,-2), (3,−2)}
1.) Set:
2.)
Table:
3.)
Graph: x y x y -3 -2 3 1

3. Range- the set of the second coordinate of each ordered pair.
Relation- a set of ordered pairs
Ex: {(-3,1), (0,-2), (3,−2)}
Domain- the set of the first coordinate of each ordered pair.
Domain = {-3, 0, 3}
Range- the set of the second coordinate of each ordered pair.
Notice how the -2 is not repeated!
Range = {1, -2}

4. Try This:
Write the Domain and Range of the following relation:
{(1,3), (5,-5), (-4,0), (2,-3), (-5,-4)}
Domain = {1, 5, -4, 2, -5}
Range = {3, -5, 0, -3, -4}

5. Function - A relation in which each coordinate in the Domain is paired with exactly one coordinate in the Range.
Are these functions?
A. {(-1,-1), (0,0), (4,-4), (5,-5)}
Yes
B. {(1,4), (0,0), (1,-2), (2,-4)} No

6. You can also think of the Domain as the Input (or x value) and the Range as the Output (or y value).
Given the function rule: y=-2x+1 and a domain = {3,2,1,0}, complete the table.
Input (x)
Output (y)
Rule -2x+1
So, you can say that the:
-2(3)+1 -5
-2(2)+1
Domain=
{3,2,1,0} -3
-2(1)+1 -1
Range=
{-5,-3,-1,1}
-2(0)+1 1

7. You can graph the function by using the Domain and the Range to write a set of ordered pairs for the function.
Domain =
{3,2,1,0}
Range =
{-5,-3,-1,1}
Set of Ordered Pairs: y x
A (3,−5) D
B (2,−3) C
C (1,−1) B
D (0 , 1) A
The points must be in a straight line.

8. Now using the table, give the:
Try This:
Given the function rule y=½x+1 and a domain = {4,2,−2,−4} complete the table.
First input the x-value (domain) into the function to find the output y-value (range).
INPUT (x)
OUTPUT (y)
½x+1
Now using the table, give the:
½(4)+1 3
½(2)+1 2
Domain=
{4,2,-2,−4}
½(-2)+1
Range=
{3,2,0,−1}
½(-4)+1 −1

9. Next:
Write a set of ordered pairs for the function and graph the function
Domain =
{4,2,−2,−4}
Range =
{3,2,0,-1}
Set of Ordered Pairs: y x A B
A (4,3) C D
B (2,2)
C (−2,0)
D (−4 ,−1)

10. Now using the table, give the:
Try This:
Given the function rule y=x−3 and a domain = {0,1,2,3}, complete the table:
First input the x-value (domain) into the function to find the output y-value (range).
INPUT (x)
OUTPUT (y)
Rule x−3
Now using the table, give the:
(0)−3 −3
(1)−3
{0,1,2,3} −2
Domain=
{-3,-2,−1,0}
(2) −3 −1
Range=
(3)−3

11. Next:
Write a set of ordered pairs for the function and graph the function
Domain =
{0,1,2,3}
Range =
{−3,−2,1,0}
Set of Ordered Pairs: y x
A (0,−3) D
B (1,−2) C B
C (2, −1) A
D (3, 0)