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Lesson: Determining Whether a Function Is Linear or Nonlinear

Linear equations appear as lines when they are graphed and have a constant slope. Nonlinear equations appear curved when graphed and do not have a constant slope. In this lesson, we will learn how to determine whether a function is linear or nonlinear.

Worksheet: Determining Whether a Function Is Linear or Nonlinear • 8 Questions

Q1:

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

x	3	6	9	12
y	32	25	18	11

Alinear function
Bnonlinear function

Q2:

The cost of a speeding ticket is a function of the speed the car was traveling. Use the table to determine whether it is a linear or nonlinear function.

Speed (mph)	70	80	90	100
Cost (dollars)	25	50	150	300

Anonlinear function
Blinear function

Q3:

The table shows the charge for a long distance call as a function of the number of minutes the call lasts. Determine whether the charge is a linear or a nonlinear function of the number of minutes.

Minutes	3	6	9	12
Cost (Cents)	51	102	153	204

Aa linear function
Ba nonlinear function

Q4:

Determine whether the given table of values must be from a nonlinear function, or could be from a linear function.

-value	0	2	4	6
-value	3	4	5	6

AIt could be from a linear function.
BIt must be from a nonlinear function.

Q5:

Determine whether the given figure represents a linear or nonlinear function.

Aa nonlinear function
Ba linear function

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