Linear and Nonlinear Functions
Identifying functions
on tables, graphs, and equations.
Warm Up
 Graph y = 2x + 1
 What is the linear
equation for this graph?
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
Equations: Linear or Nonlinear
 An equation is linear if the x value is found
in the numerator and if it has an exponent
of 1 or 0.
 If the x value is in the denominator or if it
has any other exponent, it is nonlinear
y = x3 + 1
y = 6/x
y=x+4
linear
nonlinear
y=½x
linear
nonlinear
y=4
linear
Identify:Linear or Nonlinear Equation?
y = .6x1
y = x2 + 8
y = 3x
2 +1
y = 2/x + 5
linear
nonlinear
linear
nonlinear
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
Discrete vs. Continuous
 A function is discrete if the graph has space
between possible data (graph will be
represented by dots)
 A function is continuous if the graph has no
space between data values (graph will be a
solid line)