Name
Class
Date Lesson 3-5
Nonlinear Functions
Lesson Objective
Common Core State Standard
To identify nonlinear functions
Functions: 8.F.3
Vocabulary
A quadratic function is a function in which the greatest exponent of a variable is 2.
parabola
The graph of a quadratic function is a U-shaped curve called a .
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A nonlinear function is a function whose graph is not a straight line.
Examples
1 Nonlinear Functions from Graphs Which functions appear to be nonlinear?
y
8
4
8
4
O
y
8
4
8x
4
8
4
4
4
O
8x
8
4
O
4
4
4
8
8
8
Function 1
Function 2
is not
a straight line.
The graph of function 2
is
a straight line.
The graph of function 3
is not
a straight line.
1 and 3
4
8x
Function 3
The graph of function 1
So, function(s)
y
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8
is/are nonlinear.
2 Nonlinear Functions from Tables and Equations Determine which
function is nonlinear.
a. Simplify each equation if possible.
y 5 3(x 1 4) 2 5
y 5 3x 1 7
y 5 2x3 1 5
The greatest exponent in the first function is
The greatest exponent in the second function is
The
34
441198_C3_Ch3_WKbk_Ver-1.indd 34
second
1
.
3
.
function is nonlinear because its greatest exponent is 2 or greater.
Course 3 Lesson 3-5
Daily Notetaking Guide
10/12/12 11:19 AM
Name
Class
Date
b. Find the ratios between the changes in variables for each table.
x
y
5
2
7
4
10
6
x
14
8 1, 32 , and 2
y
3
5
6
3
9
1
12
21
23
2
first
The ratios are not the same in the
nonlinear
function.
table, so it represents a
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3 Nonlinear Functions from Descriptions Decide if the function described is
linear or nonlinear.
Samantha throws a softball into the air. A function relates the height of the
ball above the ground to time.
Decide if the height per second of the ball changes at a constant rate. Explain.
No; it increases and then decreases.
nonlinear
So, this function is .
Quick Check
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1. Sketch the function that passes through the points in the table. Does the
function appear to be nonlinear?
x
y
2
4
4
8
6
12
no
8
16 2. Which of the two given functions is nonlinear?
a. y 5 17 2 4x
y 5 4 1 2(x 1 7)
b. x
y
3
3
6
5
9
7
12 10
x
6
y
22
7
1
8
4
9
7
3. John mows lawns. He charges his customers $15 per hour. A function relates the number of
hours John works and the amount he earns. Is the function nonlinear? Explain.
No. Possible explanation: as time increases by 1 hour, John’s earnings
increase by $15. The rate of change is constant which makes the
function linear.
Daily Notetaking Guide
441198_C3_Ch3_WKbk_Ver-1.indd 35
Course 3 Lesson 3-5
35
10/10/12 6:20 PM