Chapter 3: Q. 22 (page 136)

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .
x $y = f (x)$
-2 $\frac{1}{4}$
-1 $\frac{1}{2}$
0 1
1 2
2 4

Short Answer

Expert verified

The function is non linear.

Step by step solution

Step 1. Given Information

x	$y = f (x)$
-2	$\frac{1}{4}$
-1	$\frac{1}{2}$
0	1
1	2
2	4

The data in the table represent values ofy with respect tox.

Compute the average rate of change of each function.

If the average rate of change is constant, then the function is linear.
If the average rate of change is not constant, then the function is nonlinear.

Step 2. Calculation

Calculate average rate of change by the formula $\frac{∆ y}{∆ x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

x	y	$\frac{∆ y}{∆ x}$
-2	$\frac{1}{4}$	0.25
-1	$\frac{1}{2}$	0.5
0	1	1
1	2	2
2	4

Step 3. Conclusion

The average rate of change is not constant, so the function is not linear.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .
x $y = f (x)$
-2 $\frac{1}{4}$
-1 $\frac{1}{2}$
0 1
1 2
2 4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Discrete Mathematics

Geometry

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .xy=fx-214-112011224

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Discrete Mathematics

Geometry

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .
x $y = f (x)$
-2 $\frac{1}{4}$
-1 $\frac{1}{2}$
0 1
1 2
2 4