3.1 Functions & Relations

Learning Target

Student will be able to…

●Determine whether relations are functions.

●Find the domain and range of a function.

●Identify the independent and dependent variables of functions.

Vocabulary

●

A relation is a set of ordered pairs. The set of first elements (x-value)
is the domain and is the independent variable. The set of second
elements (y-values) is the range and is the dependent variable.

●

A function is a clearly defined rule that converts an input into
exactly one output. These rules often come in the form of:

(1) equations
(2) graphs
(3) tables
(4) verbal descriptions.

Example 1

Determine whether relations are functions.

(a)

{(0,0), (1,-11), (2,22), (3,-33), (4, 44)}

b)

Domain:

Range:

Domain:

Range:

c)

d)

Example 2

Given the function rule, a) identify the independent variable, b) identify the dependent
variable, find the range for the given domain values, and determine if the relation is a
function.

(a) Relation: y=5-2x Domain: {1, 2, 3}

(b) Relation: y=2|x|-1

Domain: {-2,0,4}

Example 3

The graph of a relation shows whether it is a function. If a vertical line can be drawn
through two or more points of the graph (the points have the same x-coordinate), then
the relation is not a function. This is called the vertical line test.