Download Linear and Nonlinear Functions

Linear and Nonlinear Functions
Identifying functions
on tables, graphs, and equations.
Warm Up
1. What is the slope
and y-intercept of:
2. Rewrite the linear
equation 3y + x = 9
to its slopeintercept form.
3. What is the linear
equation for this graph?
Linear Functions
 Linear Functions have
graphs that are straight lines
and represent constant rate
of change.
NonLinear Functions
 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).
Compare and Contrast
Yards to Square Yards
Number of Feet
Area of Square (yd2)
Yards to Feet
Number of Yards
Length of a Side of a Square Yard
Tables: Linear or Nonlinear
 Is the rate of change constant (the same)?
+2
+2
+2
x
y
2
50
4
35
6
20
8
5
 linear
-15
-15
-15
+3
+3
+3
x
y
1
1
4
16
7
49
10
100
 nonlinear
+15
+33
+51
Identify: Linear or Nonlinear Table?
x
y
0
20
5
16
10
12
15
8
 linear
x
0
2
4
6
y
0
2
8
18
 nonlinear
Graphs: Linear or Nonlinear
 Is the graph a straight line?
 linear
 nonlinear
 linear
Identify: Linear or Nonlinear Graph?
 linear
 linear
 nonlinear
Linear
Nonlinear
Identify:Linear or Nonlinear Equation?
y = .6x1
y = x2 + 8
y = 3x
2 +1
Linear
Nonlinear
Linear
(exponent is (exponent >1 )
0 or 1)
(y=mx+b
form)
y = 2/x + 5
Nonlinear
(variable in the
denominator)
Pointers to Keep in Mind
 A table is linear if the rate of change is constant.
There is a common difference.
 A graph is linear if it is a straight line.
 An equation is linear if the power of x is either 1
or 0 and it appears in the numerator.
Exit Slip
 Identify if linear or nonlinear.
1. Table A
3. Equation
x
3
6
9
12
y
12
10
8
6
y = x8 + 5
2. Graph
a
b
c
Exit
1. What does linear mean?
Ticket
2. Is the function linear or nonlinear?
WHY OR WHY NOT?
B
A
X
Y
X
Y
1
6
-2
2
2
8
-1
4
3
10
0
8
4
12
1
16
Practice Worksheet
Complete the practice worksheet.
Work with a partner or on your own.
Submit completed worksheet for grading.
Solutions are discussed the next day.