Module 3.2 Understanding Relations And Functions

Module 3.2 Understanding Relations

And Functions

How do you represent relations and functions?

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Definitions:

A relation is a set of ordered pairs (x, y) where x is the input value and y is the output value.

The domain is all possible inputs (or x-values) of a relation. The range is all possible outputs (or y-values) of a relation.

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For example, the following relation represents the number of whole-wheat cracker boxes sold and the money earned:

{ (1, 4) , (2, 8) , (3, 12) , (4, 16) }

1 box sold earned $4. 2 boxes sold earned $8. 3 boxes sold earned $12. 4 boxes sold earned $16.

The domain is all possible inputs: {1, 2, 3, 4} ? Number of whole-wheat cracker boxes sold The range is all possible outputs: {2, 8, 12, 16} ? Money earned

In truth, relations and functions can be represented not only as ordered pairs, but also as: 1) A table 2) A graph 3) A mapping diagram.

For the following relation, the input, X, is the ages of boys, and the output, Y, is their corresponding height, in inches.

Ordered Pairs

{ (7, 41) , (8, 45) , (9, 49) , (10, 52) , (10, 53) , (11, 55) , (12, 59) }

Table

Graph

Mapping Diagram

Domain

Range

(Can be horizontal or vertical)

What is the domain of the relation, and what does it represent? ______________

In a mapping diagram, the arrows start at the inputs, or x-values, and point to the outputs, or y-values.

What is the range of the relation, and what does it represent? _______________________

The number 10 appears twice in the x column of the table. How many times is it written in the domain? The domain is a list of the input values and a number should only be listed once no matter how many times it actually appears in the relation.

In a mapping diagram, where do the arrows start, and where do they point? They start at the inputs, or x-values, and point to the outputs, or y-values.

P. 115

P. 116

A function is a type of relation where for each input value there is only one unique output value. Example: = When x = 3, y will always be equal to 9. Question: The map for the previous example appears below. Is it a function?

P. 116

The given relation represents the number of students and the number of classrooms the school has to have for the corresponding number of students.

Ordered Pairs

{ (40, 2) , (45, 3) , (50, 4) }

Table

Graph

Mapping Diagram

Domain

Range

What is the domain of the relation, and what does it represent? ____________________________________________ What is the range of the relation, and what does it represent? _____________________________________________ This relation is a function, because each domain value is paired with exactly one range value.

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