Download Algebra 1 Lesson 5

Relations and Functions
Algebra 1
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
Relations and Functions
Lesson 5-2
Algebra 1
Additional Examples
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.
The relation is not a function.
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.
The relation is a function.
Relations and Functions
Lesson 5-2
Algebra 1
Additional Examples
Use the vertical-line test to determine whether the relation
{(3, 2), (5, –1), (–5, 3), (–2, 2)} 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.
A vertical line would not pass through more than one point, so the
relation is a function.
Vertical Line Test
Algebra 1
Relations and Functions
Lesson 5-2
Algebra 1
Additional Examples
Make a table for ƒ(x) = 0.5x + 1. Use 1, 2, 3, and 4
as domain values.
x
0.5x + 1
f(x)
1
0.5(1) + 1
1.5
2
0.5(2) + 1
2
3
0.5(3) + 1
2.5
4
0.5(4) + 1
3
Relations and Functions
Lesson 5-2
Algebra 1
Additional Examples
Evaluate the function rule ƒ(g) = –2g + 4 to find the range for
the domain {–1, 3, 5}.
ƒ(g) = –2g + 4
ƒ(–1) = –2(–1) + 4
ƒ(–1) = 2 + 4
ƒ(–1) = 6
The range is {–6, –2, 6}.
ƒ(g) = –2g + 4
ƒ(3) = –2(3) + 4
ƒ(3) = –6 + 4
ƒ(3) = –2
ƒ(g) = –2g + 4
ƒ(5) = –2(5) + 4
ƒ(5) = –10 + 4
ƒ(5) = –6