3.1 Representing Relations Objectives The student will be able to: represent relationship among quantities using tables, graphs, and diagrams identify mathematical domains and ranges identify the inverse of a relation. Indicators: PFA #1, PFA#7 Designed by Skip Tyler, Varina High School Modified by Anny Lin, Crestwood Middle School

How about some more definitions? The domain is the set of 1st coordinates of the ordered pairs. The range is the set of 2nd coordinates of the ordered pairs. A relation is a set of ordered pairs.

Given the relation {(3,2), (1,6), (-2,0)}, find the domain and range.

What would this be? {(2,4), (3,-1), (0,-4)} A lame relationship!! Ha! Ha!

The relation {(2,1), (-1,3), (0,4)} can be shown by x y 1) a table. 2) a mapping. 3) a graph. 2 -1 1 3 4 2 -1 1 3 4

Relation = {(-1,3), (0,6), (4,-1), (7,3)} Given the following table, show the relation, domain, range, and mapping. x -1 0 4 7 y 3 6 -1 3 Relation = {(-1,3), (0,6), (4,-1), (7,3)} Domain = {-1, 0, 4, 7} Range = {3, 6, -1, 3}

You do not need to write 3 twice in the range! Mapping x -1 0 4 7 y 3 6 -1 3 -1 4 7 3 6 -1 You do not need to write 3 twice in the range!

What is the domain of the relation {(2,1), (4,2), (3,3), (4,1)} {2, 3, 4, 4} {1, 2, 3, 1} {2, 3, 4} {1, 2, 3} {1, 2, 3, 4} Answer Now

What is the range of the relation {(2,1), (4,2), (3,3), (4,1)} {2, 3, 4, 4} {1, 2, 3, 1} {2, 3, 4} {1, 2, 3} {1, 2, 3, 4} Answer Now

Inverse of a Relation: For every ordered pair (x,y) there must be a (y,x). Write the relation and the inverse. -1 3 4 -6 -4 2 Relation = {(-1,-6), (3,-4), (3,2), (4,2)} Inverse = {(-6,-1), (-4,3), (2,3), (2,4)}

Write the inverse of the mapping. -3 4 3 -1 2 {(4,-3),(2,-3),(3,-3),(-1,-3)} {(-3,4),(-3,3),(-3,-1),(-3,2)} {-3} {-1, 2, 3, 4} Answer Now

http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_05/extra_examples/chapter4/lesson4_3.pdf

c. What conclusions might you make from the graph of the data? The number of departures of U.S. commercial airlines has increased each year. This may be due to the safer conditions or less expensive airline tickets.

Homework: Page 146 13-21 all and 23, 25, 27