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Chapter 3: Q. 2 (page 175)

Determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.

Short Answer

Expert verified

The function is linear and the equation of the line isf(x)=-5x+2.

Step by step solution

01

Step 1. Given information.

Determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.

02

Step 2. Step 2. Equation of line and slope of the graph.

The linear function is given by

g(x)=mx+b;m鈮�0

The slope of the graph is mand the y-intercept is b.The average rate of change is equal to the slope.

m=gx2-gx1x2-x1

The linear function have a constant average rate of change.

03

Step 3. find linear function.

Look at the given table and notice that

y5-y4=y4-y3=y3-y2=y2-y1=-5

When you changes x value for 1. So, average rate of change is constant. Then the slope is m=-5.

Also the y-intercept is b=2because that is the value of the function for x=0.

Then the equation of function is:

f(x)=-5x+2

04

Step 4. Conclusion.

The function is linear and the equation of line isf(x)=-5x+2.

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Most popular questions from this chapter

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

(e)g(x)鈮�0(f)f(x)>g(x)(g)f(x)鈮�1

f(x)=-x2+3g(x)=-3x+3

If F(x)=4,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.

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.

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

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)=3x2+6x
See all solutions

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