Relations
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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 .

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Relations
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
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?


Vocabulary summary chart

Domain

Independent Variable

x-axis

First coordinates

Range

Dependent Variable

y-axis

Second coordinates

Vocabulary Summary Chart

(x, y)


Functions
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
Inverses

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


Representations
Representations

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

    • Set of ordered pairs

    • Table

    • Graph – Review Coordinate Plane Vocabulary

    • Mapping


Mapping

X

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
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
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
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
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
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 & 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.




Summary
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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