Question

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

Short answer

The possible function is$f\left(x\right)=x(x-1)(x-2)$

Step-by-step solution

Step 1. Given information

The graph is

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:

$$\begin{gathered} x=0 \\ x=1 \\ x=2 \end{gathered}$$

So the factors of the function are: role="math" localid="1646318209936" $\left(x-0\right),\left(x-1\right),\left(x-2\right)$

At all these points the graph crosses x-axis

So each zero will have odd multiplicity

Hence the function is

$f\left(x\right)=x(x-1)(x-2)$