Relations and Functions

Vocabulary• the domain of a relation is the x-values

• the range of a relation is the y-values

• a relation is a function if no x-values repeat.

1. {(-6, -1), (-5,-9), (-3, -7), (-1,7), (6,-9)}• Domain (all of the x values):

{-6, -5, -3, -1, 6}

• Range (all of the y values):{-9, -7, -1, 7}

• Function?• Yes

2. {(1,4), (-1, 6), (5, -2), (1, -3), (6, 5)}• Domain:

{-1, 1, 5, 6}

• Range: {-3, -2, 4, 5, 6}

• Function? No

Discrete and Continuous Relations

• Discrete Relations– consists of points that are

not connected– Finite number of elements

• Continuous Relations– Can be graphed with a line

or smooth curve– Infinite number of elements

Vertical Line Test• The vertical line test is used to determine

whether the relation is a function.

• If no vertical line intersects a graph in more than one point, the graph represents a function.

• If a vertical line intersects a graph in two or more points, the graph does not represent a function.

Function?

3. The table shows the average points per game for Dwayne Wade of the Miami Heat for four seasons.

Season Dwayne Wade’s age Average Points Per Game

2003-2004 22 16.2

2004-2005 23 24.1

2005-2006 24 27.2

2006-2007 25 23.5

A. Assume that the ages are the domain. Identify the domain and range.

D= {22, 23, 24, 25}R= {16.2, 24.1, 27.2, 27.4}

B. Write a relation of ordered pairs for the data.{(22, 16.2), (23, 24.1), (24, 27.2), (25, 27.4)}

Season Dwayne Wade’s age

Average Points Per Game

2003-2004 22 16.22004-2005 23 24.12005-2006 24 27.22006-2007 25 27.4

Evaluating Functions• When an equation represents a function, the

variable x is called the independent variable.

• The other variable, y, is often called the dependent variable because its values depend on x.

• Equations that represent functions are often written in function notation. The equation

y = 5x – 1 can be written as f(x) = 5x – 1.

Evaluating Functions5. f(x) = 3x2-9

Find f(2).Find f(3).

f(2)=3(2)2-9f(3)=3(3)2-9=3(4)-9

=3(9)-9=12-9

=27-9= 3

=18