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# Relations & Functions

Introductory presentation
by

## Tabitha Durham

on 14 January 2011

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#### Transcript of Relations & Functions

Relations & Functions
What's a Relation?
What's a Function?
An Introduction to the Concepts
Definition: a set of ordered pairs
What does a Relation look like?
4 Representations
1. List/Set Notation
2. Table (Tabular Form)
3. Graph
4. Mapping
Definition: a relation in which each value of the domain is paired with a unique value in the range
IN OTHER WORDS:
Every x is paired with 1 and only 1 y
When you hit the "Coke" button on a Coke machine (input) and a Coke comes out (output), the machine is FUNCTIONing correctly.
If you hit the "Coke" button a second time (same input) and a Sprite comes out, you know the machine is NOT FUNCTIONing correctly.
How do you know if a Relation is a Function?
Associated Vocab:
Domain: set of x-values from a relation
(AKA: input, abscissa)
Range: set of y-values from a relation
(AKA: output, ordinate)
Inverse: new relation in which the values in each ordered pair have been swapped
Different "checks" for when a relation is a function
Based on how relation is represented
Mapping:
Function: 1 arrow LEAVING each value in the domain

Non-function: more than 1 arrow LEAVING any value in the domain
Table/List:
Function: each domain value paired with only 1 value in range

Non-function: any value in domain is repeated
Graph:
Function: passes Vertical Line Test

Non-function: fails Vertical Line Test
Vertical Line Test:
Pass: only 1 point is covered by a vertical line as it moves across the graphed points
Fails: 2 or more points are covered by a vertical line as it moves across the graphed points
Example: {(0,2), (3,-1), (-4,5),
(-8,5), (0,5), (3,2)}
Real-Life Example:
Full transcript