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# Relations - PowerPoint PPT Presentation

Relations. A relation is a set of ordered pairs. The first coordinates ( x ) are the domain of the relation. The domain contains all values of the independent variable .

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## PowerPoint Slideshow about 'Relations' - kyle

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Presentation Transcript

• A relation is a set of ordered pairs.

• The first coordinates (x) are the domain of the relation. The domain contains all values of the independent variable.

• The second coordinates (y) are the range of the relation. The range contains all values of the dependent variable.

• Independent Variable: The variable in a relation whose value is subject to choice.

• Dependent Variable: The variable in a relation whose value depends on the value of the independent variable.

• What examples can you think of where one thing depends on another?

Independent Variable

x-axis

First coordinates

Range

Dependent Variable

y-axis

Second coordinates

Vocabulary Summary Chart

(x, y)

• Some relations are functions.

• In a function, each member of the domain is paired with exactly one member of the range.

• x values can only go with one y

• y values can go with any number of x values

• The inverse of any relation is obtained by switching the coordinates in each ordered pair.

• A relation can be represented in different ways, such as a

• Set of ordered pairs

• Table

• Graph – Review Coordinate Plane Vocabulary

• Mapping

4

-2

-3

2

0

Y

3

-1

2

-4

Mapping

• A mapping is an easy way to determine if a relation is a function.

• Remember if your x goes to more than one y, then it is not a function.

• A mapping for the ordered pairs :

(4, 3)

(-2, 1)

(-3, 2)

(2, -4)

(0, -4)

Example 1a: List the domain and range for each relation. Is each relation a function? Explain. Make a t

• (0, 5), (1, 6), (2, 4), (3, 7)

Domain: ____________

Range: ____________

Example 1b: List the domain and range for each relation. Is each relation a function? Explain.

• (0, 5), (1, 5), (2, 6), (3, 7)

Domain: ____________

Range: ____________

Example 1c: List the domain and range for each relation. Is each relation a function? Explain.

• (0, 5), (0, 6), (1, 6), (2, 7)

Domain: ____________

Range: ____________

Express the relation {(4, 3), (–2, –1), (–3, 2), (2, –4), (0, –4)} as a table, a graph and a mapping.

a. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)} as a table, a graph, and a mapping.

b. Determine the domain and range.

c. Write the inverse of the relation.

• Graphing a relation on a coordinate plane gives us a visual way to tell whether the relation is a function.

• Vertical Line Test

• If a vertical line can be drawn so it intersects the graph at two or more points (at the same time), then the relation is not a function.

• Is every relation a function? ____

• Is every function a relation? ____

• Function or not

• May x go to two different y’s? ____

• May y go to two different x’s? ____

• Domain vs. Range Chart

• What are the different ways to represent a relation?

• What is the Vertical Line Test?