#### 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