Author: mark_cameron
Last saved by: MHE
Company: McGraw-Hill

Lesson 12-1

Example 1 Identify Functions Using Graphs
Determine whether the graph represents a linear or nonlinear function. Explain.

The graph is a curve, not a straight line. So it represents a nonlinear function.

Example 2 Identify Functions Using Graphs
Determine whether the graph represents a linear or nonlinear function. Explain.

The graph is a straight line. So it represents a linear function.

Example 3 Identify Functions Using Equations
Determine whether y = 2x + 1 represents a linear or nonlinear function. Explain.

This equation is linear since it is of the form y = mx + b.

Example 4 Identify Functions Using Equations
Determine whether y = x^2 represents a linear or nonlinear function. Explain.

Since x is raised to the second power, the equation cannot be written in the form
y = mx + b.  So this function is nonlinear.

Example 5 Identify Functions Using Tables
x | y
2 | 18
3 | 22
4 | 26
5 | 30
Determine whether the table represents a linear or nonlinear function. Explain.

As x increases by 1, y increases by 4 each time. The rate of change is constant, so this function is linear.

x | y
2 | 5
3 | 10
4 | 17
5 | 26
Example 6 Identify Functions Using Tables
Determine whether the table represents a linear or nonlinear function. Explain.

As x increases by 1, y increases by a greater amount each time. The rate of change is not constant, so this function is nonlinear.
Hours | Pay
21 | $105
23 | $115
25 | $125
27 | $135
29 | $145

Example 7 Real-World Example
WORKING Use the table to determine whether the amount of pay is a linear function of the hours worked.

Examine the differences between the amount of pay for each amount of hours worked.

$115 – $105 = $10	$125 – $115 = $10	$135 – $125 = $10	$145 – $135 = $10

Then examine the difference between the corresponding numbers of hours.

23 – 21 = 2	25 – 23 = 2  	27 – 25 = 2	29 – 27 = 2	

As the number of hours increases by 2, the amount of pay increases by $10 each time. The rate of change is constant, so this function is linear.