Algebra 1

Relations and Functions

A Relation is a set of ordered pairs.

The Domain of a relation is the set of first coordinates of the ordered pairs.

The Range is the second coordinates.

A Function is a relation that assigns exactly one value in the range to each value in the domain. (Each X has only one Y)

Domain = X’s = Input

Range = Y’s = Output

Algebra 1

Determine whether each relation is a function.

a. {(4, 3), (2, –1), (–3, –3), (2, 4)}

The domain value 2 corresponds to two range values, –1 and 4.

b. {(–4, 0), (2, 12), (–1, –3), (1, 5)}

There is no value in the domain that corresponds to more than one value of the range.

Lesson 5-2

The relation is not a function.

The relation is a function.

Relations and Functions

Additional Examples

Algebra 1Lesson 5-2

Use the vertical-line test to determine whether the relation {(3, 2), (5, –1), (–5, 3), (–2, 2)} is a function.

A vertical line would not pass through more than one point, so the relation is a function.

Step 1: Graph the ordered pairs on a coordinate plane.

Step 2: Pass a pencil across the graph. Keep your pencil straight to represent a vertical line.

Relations and Functions

Additional Examples

Algebra 1

Vertical Line Test

Algebra 1

Make a table for ƒ(x) = 0.5x + 1. Use 1, 2, 3, and 4as domain values.

Lesson 5-2

x 0.5x + 1 f(x)1 0.5(1) + 1 1.5

2 0.5(2) + 1 2

3 0.5(3) + 1 2.54 0.5(4) + 1 3

Relations and Functions

Additional Examples

Algebra 1

Evaluate the function rule ƒ(g) = –2g + 4 to find the range for the domain {–1, 3, 5}.

The range is {–6, –2, 6}.

ƒ(g) = –2g + 4ƒ(5) = –2(5) + 4ƒ(5) = –10 + 4ƒ(5) = –6

ƒ(g) = –2g + 4ƒ(–1) = –2(–1) + 4ƒ(–1) = 2 + 4ƒ(–1) = 6

ƒ(g) = –2g + 4ƒ(3) = –2(3) + 4ƒ(3) = –6 + 4ƒ(3) = –2

Lesson 5-2

Relations and Functions

Additional Examples