Main Idea and New Vocabulary

Example 1: Identify Functions Using Tables

Example 2: Identify Functions Using Tables

Example 3: Real-World Example: Linear and Nonlinear Functions

Example 4: Real-World Example: Linear and Nonlinear Functions

• Determine whether a function is linear or nonlinear.

• nonlinear function

Identify Functions Using Tables

Determine whether the table represents a linear or nonlinear function. Explain.

As x increases by 2, y increases by a greater amount each time. The rate of change is not constant, so this function is nonlinear.

Identify Functions Using Tables

Answer: The function is nonlinear.

Check Graph the points on a coordinate plane.

The points do not fall in a line. The function is nonlinear.

Determine whether the table represents a linear or nonlinear function. Explain.

A. Linear; the rate of change is not constant.

B. Linear; the rate of change is constant.

C. Nonlinear; the rate of change is not constant.

D. Nonlinear; the rate of change is constant.

Determine whether the table represents a linear or nonlinear function. Explain.

Identify Functions Using Tables

As x increases by 3, y increases by 9 each time. The rate of change is constant, so this function is linear.

Identify Functions Using Tables

Answer: The function is linear.

Check Graph the points on a coordinate plane.

The points fall in a line. The function is linear.

Determine whether the table represents a linear or nonlinear function. Explain.

A. Linear; the rate of change is constant. As x increases by 1, y increases by 4.

B. Linear; the rate of change is constant. As x increases by 2, y increases by 12.

C. Linear; the rate of change is constant. As x increases by 3, y increases by 16.

D. Nonlinear; the rate of change is not constant.

CLOCKS Use the table below to determine whether or not the number of revolutions per hour of a second hand on a clock is a linear function of the number of hours that pass.

Linear and Nonlinear Functions

Examine the differences between the number of second hand revolutions each hour.

Linear and Nonlinear Functions

120 – 60 = 60 180 – 120 = 60240 – 180 = 60 300 – 240 = 60

The difference in second hand revolutions is the same. As the number of hours increases by 1, the number of second hand revolutions increases by 60. Therefore, this function is linear.

Answer: The function is linear.

Check Graph the data to verify the ordered pairslie on a straight line.

Linear and Nonlinear Functions

GEOMETRY Use the table below to determine whether or not the perimeter of a square is a linear function of the length of its side.

A. Linear; the rate of change is constant. As the length of the side increases by 1, the perimeter increases by 4.

B. Linear; the rate of change is constant. As the length of the side increases by 1, the perimeter increases by 6.

C. Linear; rate of change is constant. As the length of the side increases by 4, the perimeter increases by 1.

D. Nonlinear; the rate of change is not constant. As the length of the side increases by 4, the perimeter increases by a greater amount each time.

MAZE At the first level of a maze, there are three possible paths that can be chosen. At the next level, each of those three paths have three more possible paths. Does this situation represent a linear or nonlinear function? Explain.

Linear and Nonlinear Functions

Make a table to show the number of possible paths starting with Level 1.

Graph the function.

The data do not lie on a straight line.

Linear and Nonlinear Functions

Answer: This function is nonlinear.

MONEY Diante puts $10 in his savings account. The next month he doubles the amount and puts $20 in his account. The third month he double the amount again and puts $40 in his account. Does this situation represent a linear or a nonlinear function? Explain.

A. Linear; the data lie on a straight line.

B. Linear; the data do not lie on a straight line.

C. Nonlinear; the data lie on a straight line.

D. Nonlinear; the data do not lie on a straight line.