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Chapter 3: Q. 26 (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)
-2-4
-1-3.5
0-3
1-2.5
2-2

Short Answer

Expert verified

The function is linear and the equation of the line isf(x)=0.5x-3

Step by step solution

01

Step 1. Given Information  

Given data is

xy=f(x)
-2-4
-1-3.5
0-3
1-2.5
2-2

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
-2-40.5
-1-3.50.5
0-30.5
1-2.50.5
2-2

The average rate of change is constant, so the function is linear.

03

Step 3. Find equation of line.  

The average rate of change is m=0.5and a point from given data (-2,-4).

Use slope point form to find equation of the line.

y-y1=m(x-x1)y-(-4)=0.5(x-(-2))y+4=0.5(x+2)y+4=0.5x+1y=0.5x-3

04

Step 4. Conclusion  

As average rate of change is constant, so function is linear and the equation of the line is f(x)=0.5x-3

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Most popular questions from this chapter

Match each graph to one the following functions.

f(x)=-x2-1

If p(x)=-x+6,then

(a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant.

On one set of coordinate axes, graph the family of parabolas f(x)=x2+bx+1for b = -4, b = 0, and b = 4. Describe the general characteristics of this family.

In Problems 25鈥�32, use the given functions f and g.

(a)f(x)=0(b)g(x)=0(c)f(x)=g(x)(d)f(x)>0

role="math" localid="1646199855131" (e)g(x)鈮�0(f)f(x)>g(x)(g)f(x)鈮�1

True or False The slope of a nonvertical line is the average rate of change of the linear function.
See all solutions

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