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

Variables

- 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)

Functions

- 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

Inverses

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

Representations

- 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 & the Vertical Line Test

- 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.

Example 3a: Graph the relation shown in the table. Is it a function? Explain.

Example 3b: Graph the relation shown in the table. Is it a function? Explain.

Summary

- 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?

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