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.

VariablesIndependent 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

DomainIndependent Variablex-axisFirst coordinates

RangeDependent Variabley-axisSecond coordinates

(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

MappingA 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)

X

4

-2

-3

2

0

Y

3

-1

2

-4

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

a. (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.

b. (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.

c. (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.

Domain

Range

-3 5

-5 3

3 5

5 3

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

Domain

Range

-3 -1

2 -1

-4 0

2 4

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 ChartWhat are the different ways to represent a relation?What is the Vertical Line Test?