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Chapter 4: Q. 65 (page 195)

In Problems 65–68, construct a polynomial function that might have the given graph. (More than one answer may be possible.)

Short Answer

Expert verified

The possible function isf(x)=x(x-1)(x-2)

Step by step solution

01

Step 1. Given information

The graph is

02

Step 2. To find the possible function from graph.

In the given graph we can see that there are 3 zeros because the graph is crossing the x-axis at three different points:

x=0x=1x=2

So the factors of the function are: role="math" localid="1646318209936" x-0,x-1,x-2

At all these points the graph crosses x-axis

So each zero will have odd multiplicity

Hence the function is

f(x)=x(x-1)(x-2)

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Most popular questions from this chapter

Find the real zeros of f. Use the real zeros to factor f.

f(x)=3x3-7x2+12x-28

True or False. If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients give rise to the horizontal asymptote.

Find a rational function that might have the given graph.

Graph each rational function using transformations.

F(x)=2-1x+1

In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=-4x3-x2+x+2
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