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Chapter 4: Q. 68 (page 195)

In Problems 65鈥�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 is f(x)=-12x+1x-1x-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

x=-1,1,2, so these zeros have odd multiplicity

So the factors of the function are:

x+1,x-1,x-2

the function is

role="math" localid="1646322635488" f(x)=ax+1x-1x-2

03

Step 3. To find value of a

Since,f(0)=-1

hence

-1=a(0+1)(0-1)(0-2)-1=a(1)(-1)(-2)-1=2aa=-12

so the function is

f(x)=-12x+1x-1x-2

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