# You can use a function table to determine whether ordered pairs describe a linear or nonlinear relationship

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```					 12-6 Nonlinear Functions

Course 2
12-6 Nonlinear Functions

Warm Up
Tell the slope and y-intercept of each line,
given the equation.
1. y = –8x + 7    –8; 7
2. y = 1 x – 1    1 ; –1
7          7
3. y = 9x         9; 0
4. y = – 2 x + 5 – 2 ; 5
3         3

Course 2
12-6 Nonlinear Functions

As you inflate a balloon, its volume increases.
The table below shows the increase in volume of
a round balloon as its radius changes. Do you
think a graph of the data would or would not be
a straight line? You can make a graph to find out.

A nonlinear function is a function whose graph
is not a straight line.

Course 2
12-6 Nonlinear Functions

Example 1A & 1B: Identifying Graphs of Nonlinear
Functions
Tell whether the graph is linear or nonlinear.
A.                            B.

The graph is not a straight   The graph is a straight
line, so it is nonlinear.     line, so it is linear.
Course 2
12-6 Nonlinear Functions

Example 1C & 1D: Identifying Graphs of Nonlinear
Functions
Tell whether the graph is linear or nonlinear.

C.                         D.

The graph is a straight   The graph is not a
line, so it is linear.    straight line so, it is
nonlinear.
Course 2
12-6 Nonlinear Functions

Try This: Example 1A & 1B
Tell whether the graph is linear or nonlinear.

A.              y            B.             y
4                           4

x                           x
–4    0       4             –4    0       4

–4                          –4

The graph is a straight       The graph is not a straight
line, so the graph is linear. line, so it is nonlinear.

Course 2
12-6 Nonlinear Functions

Try This: Example 1C & 1D
Tell whether the graph is linear or nonlinear.

C.              y            D.             y
4                           4

x                           x
–4    0       4             –4    0       4

–4                          –4

The graph is a straight       The graph is not a straight
line, so the graph is linear. line, so it is nonlinear.

Course 2
12-6 Nonlinear Functions

You can use a function table to determine
whether ordered pairs describe a linear or
nonlinear relationship.

For a function that has a linear relationship,
when the difference between each successive
input value is constant, the difference between
each corresponding output value is constant.

For a function that has a nonlinear relationship,
when the difference between each successive
input value is constant, the difference between
each corresponding output value varies.

Course 2
12-6 Nonlinear Functions
Example 2A: Identifying Nonlinear Relationships in
Function Tables
Tell whether the function in the table has a
linear or nonlinear relationship.
A.              Input   Output
1        2
difference = 1                          difference = 3
2        5
difference = 1                          difference = 6
3       11

The difference between            The difference between
consecutive input values          consecutive output
is constant.                      values is not constant.
The function represented in the table is nonlinear.
Course 2
12-6 Nonlinear Functions
Example 2B: Identifying Nonlinear Relationships in
Function Tables
Tell whether the function in the table has a
linear or nonlinear relationship.
A.              Input   Output
1       3
difference = 1                          difference = 3
2       6
difference = 1                          difference = 3
3       9

The difference between            The difference between
consecutive input values          consecutive output
is constant.                      values is constant.
The function represented in the table is linear.
Course 2
12-6 Nonlinear Functions
Try This: Example 2A

Tell whether the function in the table has a
linear or nonlinear relationship.
A.               Input   Output
1       1
difference = 1                          difference = 3
2       4
difference = 1                          difference = 5
3       9

The difference between            The difference between
consecutive input values          consecutive output
is constant.                      values is not constant.
The function represented in the table is nonlinear.
Course 2
12-6 Nonlinear Functions
Try This: Example 2B

Tell whether the function in the table has a
linear or nonlinear relationship.
A.               Input   Output
1       2
difference = 1                          difference = 2
2       4
difference = 1                          difference = 2
3       6

The difference between            The difference between
consecutive input values          consecutive output
is constant.                      values is constant.
The function represented in the table is linear.
Course 2
Insert Lesson Title
12-6 Nonlinear FunctionsHere

Assignment:
pg. 630-631 1-14 All

Course 2

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