1

Linear and Nonlinear Functions

How do you identify, compare, and contrast functions as linear

or nonlinear?

SPI 0806.3.7/ CC 8.F.3

� Linear Functions have graphs that are straight lines and represent constant rate of change.

� Nonlinear Functions have graphs that are not straight lines.

� The rate of change is not constant (values don’t increase/decrease at the same rate).

� Linear Functions represent constant rate of change.

� Nonlinear Functions do not represent constant rate of change.

XX YY

1 6

2 8

3 10

4 12

XX YY

-2 2

-1 4

0 8

1 16

14

x 3 6 9 12

y 12 10 8 6

15

• In slope-intercept form, x may not be raised to a power higher than 1.

• X may not appear in the denominator of a fraction.

• No additional symbols with the x.

y = x + 4

y = 6/xy = 4

y = x3 + 1y = ½

xlinearnonlinear

linear

nonlinear

linear

16

y = .6x1

17

y = 2/x + 5

18

y = x2 + 8

19

Y = 2/x + 1

20

Let's Review!!!

A. B.

Course 2

12-6 Nonlinear Functions

C. D.

Course 2

12-6 Nonlinear Functions

yE. F.

x–4

–4

4

4

0x

–4

–4

4

4

0

y

Course 2

12-6 Nonlinear Functions

yG. H.

x–4

–4

4

4

0x

–4

–4

4

4

0

y

Course 2

12-6 Nonlinear Functions

I.Input Output

1 2

2 5

3 11

Course 2

12-6 Nonlinear Functions

J.Input Output

1 3

2 6

3 9

Course 2

12-6 Nonlinear Functions

K.

Input Output

1 1

2 4

3 9

Course 2

12-6 Nonlinear Functions

L.Input Output

1 2

2 4

3 6

Course 2

12-6 Nonlinear Functions

29

Course 2

12-6 Nonlinear Functions

M.

30

Course 2

12-6 Nonlinear Functions

N.

31

Course 2

12-6 Nonlinear Functions

O.

5/x - 15 = y

32

Course 2

12-6 Nonlinear Functions

P.

6x + 2 = y

33

Exit SlipIdentify if linear or nonlinear AND

WHY.1. Table A

2. Graph

3. Equation x 3 6 9 12

y 12 10 8 6

a b c

y = + 5

8x