6th Grade Math Textbook, Fundamentals

 &KDSWHU

13-8

Method 1 Find the Slope

Find the slope to determine if the function

has a constant rate of change or a variable

rate of change.

Choose any two points from the data, and

find the slope. Then to determine if the slope

is constant or variable, find the slope using

another pair of points.

Use (0, 1) and (1, 2).  1

Use (1, 2) and (2, 4).  2

Since the slopes are different, the data

represents a nonlinear function.

2

1

4  2

2  1

y 2 y 1

x 2 x 1

1

1

2  1

1  0

y 2 y 1

x 2 x 1

Method 2 Examine the Graph

The graph is not a straight line.

The graph gets steeper and steeper as

the x-values increase.

This is a graph of a nonlinear function.

0

y

x

1452 3

4

2

6

8

10

12

14

16

Nonlinear Functions

Objective To differentiate linear functions from nonlinear functions• To use a table of

values to graph a nonlinear function on a coordinate plane• To use technology to graph a

simple quadratic equation

Joelle’s mother is a microbiologist. Over a number of days, she
records the number of cells in a sample to track the sample’s
growth. Joelle examines the data and decides to help her mother
by making a table and plotting the data on a coordinate plane.
Does the data represent a linear function or a nonlinear function?

A is a function that does nothave a constant rate

of change. The graph of a nonlinear function is nota straight line.

Nonlinear functions may involve equations like y|x|, y ,

yx^2 , and y.

To determine if a function is linear or nonlinear, analyze the

rate of change (the slope) or the graph of the function.

t, time (days) 0123456

c, number of cells 1248163264

x

nonlinear function

1

x

The quadratic function and the absolute-value function

are examples of nonlinear functions.

A , when graphed on

a coordinate plane, takes the form of a

—a U-shaped curve—that can

open either up or down. The graph at the

right shows the quadratic function yx^2.

parabola

quadratic function

0

y

x

^1423

1

 2

 3

 4

1

2

3

4

 4  3  2  1