Relations, Lines & Functions

8TH GRADE

Definition

A RELATION is a set of ordered pairs (like the x-and y-coordinates are in a "relationship". In addition, all of the x-coordinates are called the DOMAIN and all of the y-coordinates are called the RANGE.

Example: Name the domain and range for this relation below

(-5, -3), (-2,0), (1,3), (4,6), (7,9)

Domain (all the x-values): {-5, -2, 1, 4, 7}

Range (all the y-values): {-3, 0, 3, 6, 9}

Multiple Choice

Which numbers make up the domain of this relation below:

(7, 5), (-3, 2), (1,- 1), (4, -6), (-2, 4)

• {1, 2, 3, 4, 5}

• { -3, 1, 7}

• {-3, -2, 1, 4, 7}

• {-6, -1, 2, 4, 7}

Functions

A relation can be any kind of relationship between sets of numbers, FUNCTIONs are a special kind of relationship where EVERY INPUT MUST HAVE EXACTLY ONE OUTPUT.

In other words, the x-value cannot repeat

Multiple Choice

Does the relation below a function:

{(–7, 4), (–8, 3), (–7, 7), (–20, 8), (5, 9), (3, 1), (2, 6)}

• Yes

• No

Multiple Choice

Does the relation below represent a function:

{(10, 9), (–2, –16), (–6, 7), (5, 8), (8, –16), (–11, 9)}

• Yes

• No

Does this graph represent a function?

Vertical Line Test

You can easily determine if a relation is a function by graphing it and doing a vertical line test. Just draw a vertical line (or two) on the graph - if your vertical line ever touches two points of the relation, it's not a function. In other words, the vertical line test proves that none of the x-values repeat, and a relation is a function if none of the domain numbers (x-coordinates) repeat.

Examples

Multiple Choice

Is the relation shown in the table a function?

• Yes

• No

You can graph the table too.

If we took the relation from the table and graphed it, this is what it would look like.

Did it pass the vertical line test?

Yes. Therefore, the relation is a function.

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Multiple Choice

Is the relation shown in the table a function?

• Yes

• No

Graph the relation given in the table.

Did it pass the vertical line test?

No. Therefore, this relation is not a function.

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