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Chapter 3: Q. 25 (page 137)

In Problems 21鈥�28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .

xy=f(x)
-2-26
-1-4
02
1-2
2-10

Short Answer

Expert verified

The function is non linear.

Step by step solution

01

Step 1. Given Information   

xy=f(x)
-2-26
-1-4
02
1-2
2-10

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.
02

Step 2. Calculation 

Calculate average rate of change by the formula 鈭�y鈭�x=y2-y1x2-x1

xy鈭�y鈭�x
-2-2622
-1-42
02-4
1-2-8
2-10
03

Step 3. Conclusion 

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

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Most popular questions from this chapter

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=x2+4x+2

In problems 3-6, use the figure to solve each inequality.

a) f(x)>0

b)f(x)鈮�0

List the intercepts of the equation y=x2-9.

Match each graph to one the following functions.

f(x)=x2-2x+1

To graph y=(x-4)2, you shift the graph of y=x2to the ______ a distance of ______ units.
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