Question

f(x)A6X-868Which of the given functions could this graph represent?OA. f(t) = (x - 1)(x - 2)(x + 1)(x + 2)O B. f(x) = x(x - 1)(1 + 1)Oc. /(x) = x(x - 1)(x - 2)(x + 1)(x + 2)OD. (r) = x(x - 1)(x - 2)

Answer 1

The Solution:

Given the graph below:

We are required to determine the function that best describes the above graph.

Step1:

Identify the roots of the function from the given graph.

`\begin{gathered} x=-2 \\ x=-1 \\ x=1 \\ x=2 \end{gathered}`

This means that:

`\begin{gathered} x+2=0 \\ x+1=0 \\ x-1=0 \\ x-2=0 \end{gathered}`

So, the required function becomes:

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

Therefore, the correct answer is [option A]