Functions & Relations

{(-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

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}

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}

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

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 3 2 1 0 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

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.

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 4 2 -2 -4 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

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)

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 0 1 2 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

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)