1 linear and nonlinear functions how do you identify, compare, and contrast functions as linear or...
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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