Chapter 8 Section 1: Relations and Functions February 4 th , 2009

What two forms of information is being illustrated? Write in your Notes!

Graph 1: The Population of New York City, 1790-1840

Food for Life Canned Food Drive The information in this chart can be written as an ordered pair , also known as a RELATION. 150 21 106 74 20 105 195 22 104 148 24 103 216 22 102 133 25 101 Number of Cans Number of Students Home-room

Relation  Ordered Pair In the case of the Food Drive, the number of Students is the X coordinate and the Number of Cans is the Y coordinate. Room 101: (25, 133) Room 102: (22, 216) Room 103: (24, 148) Y X 150 21 106 74 20 105 195 22 104 148 24 103 216 22 102 133 25 101 Number of Cans Number of Students Home-room

In the case of the Food Drive, the number of Students is the X coordinate and the Number of Cans is the Y coordinate.

Room 101: (25, 133)

Room 102: (22, 216)

Room 103: (24, 148)

They’re All Related If all you have is a bunch of ordered pairs , you know they belong to the same RELATION if they’re in braces, or these things { }. *Back to the Relation* (Domain, Range) The first number is called the DOMAIN. The second number is called the RANGE.

If all you have is a bunch of ordered pairs , you know they belong to the same RELATION if they’re in braces, or these things { }.

*Back to the Relation*

(Domain, Range)

The first number is called the DOMAIN.

The second number is called the RANGE.

Some Relations are Functions If the DOMAIIN is PAIRED with EXACTLY ONE member of the RANGE , then the Relation is a FUNCTION. A Mapping Diagram can be used to determine if your Relation is really a Function .

If the DOMAIIN is PAIRED with EXACTLY ONE member of the RANGE , then the Relation is a FUNCTION.

A Mapping Diagram can be used to determine if your Relation is really a Function .

Mapping Diagram {(0,1), (1,2), (1,3), (2,4)} List the domain values and the range values in order. Draw arrows from the domain values to their range values. There are two range values for the domain value of 1. Therefore, this relation is NOT a function.

{(0,1), (1,2), (1,3), (2,4)}

List the domain values and the range values in order.

Draw arrows from the domain values to their range values.

There are two range values for the domain value of 1. Therefore, this relation is NOT a function.

So, If You Missed It The First Time. One range value for each domain value, then the relation is a function. More than one range value for each domain, then the relation is NOT a function.

One range value for each domain value, then the relation is a function.

More than one range value for each domain, then the relation is NOT a function.

Make a Map, Is it a Function? {(0,1), (1,2), (2,2), (3,4)} {(0,1), (1,3), (2,2), (3,4)} {(-2, 3), (2,2), (2, -2)} {(-5, -4), (0, -4), (5, -4)} Is a Function Is a Function Is NOT a Function Is a Function

{(0,1), (1,2), (2,2), (3,4)}

{(0,1), (1,3), (2,2), (3,4)}

{(-2, 3), (2,2), (2, -2)}

{(-5, -4), (0, -4), (5, -4)}

Real Life: Thinking, Instead of Math Is the time needed to cook a turkey a function of the weight of the turkey? The time the turkey cooks (RANGE VALUE) is determined by the weight of the turkey (DOMAIN VALUE). This relation is a function.

Is the time needed to cook a turkey a function of the weight of the turkey?

The time the turkey cooks (RANGE VALUE) is determined by the weight of the turkey (DOMAIN VALUE). This relation is a function.

Try These For the United States Postal Service, is package weight a function of the postage paid to mail the package? NO; a specific postage cost (Domain) can mail packages of different weights (Range). When building a wooden structure, is the amount of wood needed a function of the height of the building? YES; the higher the building, the more wood you need.

For the United States Postal Service, is package weight a function of the postage paid to mail the package?

NO; a specific postage cost (Domain) can mail packages of different weights (Range).

When building a wooden structure, is the amount of wood needed a function of the height of the building?

YES; the higher the building, the more wood you need.

Graphing Relations and Functions By graphing a RELATION on a Coordinate Plane, you can SEE whether a Relation is really a FUNCTION. Once you’ve graphed the Relations, IF the graph PASSES the Vertical Line test , then it’s a FUNCTION . If the graph does NOT pass the Vertical Line test, then the Relation is NOT a Function .

By graphing a RELATION on a Coordinate Plane, you can SEE whether a Relation is really a FUNCTION.

Once you’ve graphed the Relations, IF the graph PASSES the Vertical Line test , then it’s a FUNCTION .

If the graph does NOT pass the Vertical Line test, then the Relation is NOT a Function .

This is the Vertical-Line Test… Graph each coordinate in the Relation. Pass a pencil across the graph. Keep the pencil vertical (parallel to the Y-axis) to represent the vertical line. If the pencil covers up more than one point (one ordered pair) at once, then the RELATION is NOT a FUNCTION. Pencil passes (2,0) and (2,3), so this relation is NOT a function. -4 5 3 4 3 2 0 2 -3 -4 Range Domain

Graph each coordinate in the Relation.

Pass a pencil across the graph. Keep the pencil vertical (parallel to the Y-axis) to represent the vertical line.

If the pencil covers up more than one point (one ordered pair) at once, then the RELATION is NOT a FUNCTION.

Come to the Board Graph these Relations, is it a function or not, according to the Vertical-Line Test. 3 4 7 5 0 1 -2 0 -2 -3 -5 -6 Range Domain 5 0 5 1 3 -1 -1 -1 6 -2 4 -7 Range Domain 4 1 4 2 0 0 4 -3 4 -4 4 -5 Range Domain

Graph these Relations, is it a function or not, according to the Vertical-Line Test.

Assignment #1 Assignment #1: Pages 389-390: 1-23 all, 28, 29. If it asks for an example or explanation, you MUST give one! A good way to explain is to give the two ordered pairs that make the relation NOT a function.

Assignment #1:

Pages 389-390: 1-23 all, 28, 29.

If it asks for an example or explanation, you MUST give one!

A good way to explain is to give the two ordered pairs that make the relation NOT a function.