Chapter 3: Q. 23 (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 -8
-1 -3
0 0
1 1
2 0

Short Answer

Expert verified

The function is non linear.

Step by step solution

Step 1. Given Information

x	$y = f (x)$
-2	-8
-1	-3
0	0
1	1
2	0

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	-8	5
-1	-3	3
0	0	1
1	1	-1
2	0

Step 3. Conclusion

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

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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 -8
-1 -3
0 0
1 1
2 0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Conclusion

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In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.xy=f(x)-2-8-1-3001120

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

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

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Geometry

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 -8
-1 -3
0 0
1 1
2 0