xy ? {(3,-2), (5,4), (-2,0)}

A relation is set of ordered pairs, where one number is mapped to another number.

We need to be able to show relations in a variety of forms. In each form, there are pairs of numbers, where one number is considered the input and the other is the output.

I. Mappings A Mapping looks like this: This mapping contains three pairs: 3 is mapped onto -2 5 is mapped onto 4 -2 is mapped onto 0

II. Tables A Table looks like this: This relation contains the same pairs as the mapping we just saw. (The names at the top of the table do NOT have to be x and y!) xy

III. Coordinate Graphs A Coordinate Graph looks like this: To plot pairs on a coordinate plane, the first number tells you how far to the right or left of the origin to go, the second number is up or down. (3,-2) (5, 4) (-2,0)

IV. Sets of Ordered Pairs A Set of Ordered Pairs looks like this: We always put sets in braces { } and separate elements by commas. The order is easy to determine here! {(3,-2), (5,4), (-2,0)}

V. Input-Output Machines An Input-Output Machine looks like this: The arrows show which number is the first number (the input) and which is the second (the output). ? 3 -2

Re-Writing Relations This relation is in mapping form. Write a table for this relation ab 7 NOTE:Some relations use the same values more than once.

Re-Writing Relations This relation is in set form. Draw a mapping for this relation. {(1, 5), (0, 4), (4, 8), (-7, -3)}

The last relation had a pattern to it. Did you notice? {(1, 5), (0, 4), (4, 8), (-7, -3)} Some relations are created by some set of operations, a formula that maps one number to another number.

Formula Relations {(1, 5), (0, 4), (4, 8), (-7, -3)} In each pair, the second number is 4 more than the first number, the formula for this relation could be written: y = x + 4. Or use different letters: w = r + 4.

A Formula Machine x Input: Output:

What formula creates this relation?

This relation follows a formula, find the formula & decide what 3 maps onto.

The formula is “add 17 to each input”, x maps onto 20.

What number maps onto 0?

Find the output values if the input values are {1, 3, 5, 7}. InputOutput

Find the output values if the input values are {1, 3, 5, 7}. InputOutput

Find the output values if the input values are {1, 3, 5, 7}. InputOutput

Find the output values if the input values are {1, 3, 5, 7}. InputOutput