4.3 Patterns and nonlinear
functions
Identify and represent patterns that
describe nonlinear functions.
Interpreting graphs
Linear function: a function
whose graph is a nonvertical line.
Nonlinear: a function whose
graph is not a line
The area A, in square inches of a pizza is a function of its radius r, in inches. The cost C,
in dollars, of the sauce for a pizza is a function of the weight w, in ounces, of sauce
used. Graph these functions shown by the tables below. Is each function linear or
There is a
nonlinear?
There is a
connection/relationship
Sauce Cost
Pizza Area
connection/
between the area and the
relationship
Radius (in), r Area (in2), A radius.
Weight(oz) , w Cost, C
between the
2
12.57
2
$.80
cost and
weight of
4
50.27
4
$1.60
the sauce.
6
113.10
6
$2.40
8
201.06
8
$3.20
10
314.16
10
$4.00
Sauce Cost
Pizza Area
A
R
E
A
300
200
100
nonlinear
C
O
S
T
6
4
2
linear
(in2)
0 2 4 6 8 10
Radius (in)
0 2 4 6 8 10
Weight (oz)
The table shows the total number of blocks in each figure below as a function of the
number of blocks on one edge. What is a pattern you can use to complete the table
Represent the relationship using words, an equation, and a graph.
Words:
The total number of blocks y is the
cube of the number of blocks on
one edge x.
Equation:
y = x3
graph
12
1
13
22
4
23
2
3
9
3
42
16
52
3
3
1
8
27
4
64
25
53
125
62
36
63
216
72
49
73
343
82
64
21
2
22
4
23
8
24
16
25
32
26
64
27
128
28
256
Writing a rule to describe a nonlinear function.
The ordered pairs (1,2), (2,4), (3,8), (4,16), and (5,32) represent a
function. What is a rule that represents this function?
X
1
2
3
4
5
Y
2
4
8
16
32
y=
x
2
Assignment:
Pg 250: 6-20, 26-29
Hint:
a. 12-18 all have exponents in the equation.
b. 14, 16 have fractions in your answer.