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Chapter 4: Q. 67 (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 is $f (x) = - \frac{1}{2} (x + 1) {(x - 1)}^{2} (x - 2)$

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

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

and touches x-axis at $x = 1$

so it has even multiplicity.

So the factors of the function are:

$(x + 1), {(x - 1)}^{2}, (x - 2)$

the function is $y = a (x + 1) {(x - 1)}^{2} (x - 2)$

03

Step 3. To find value of a

Since, $f (0) = 1$

hence

role="math" localid="1646321911044" $1 = a (0 + 1) {(0 - 1)}^{2} (0 - 2) 1 = a (1) {(- 1)}^{2} (- 2) 1 = - 2 a a = - \frac{1}{2}$

so the function is

$f (x) = - \frac{1}{2} (x + 1) {(x - 1)}^{2} (x - 2)$

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Most popular questions from this chapter

Find the domain of the rational function.

$G (x) = \frac{6}{(x + 3) (4 - x)}$

In Problems 63–72, find the real solutions of each equation.

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See all solutions

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