Question

Which function does this graph correspond to?

A x(x − 1)(x + 1)



B x(x − 1)(x − 2)(x + 1)(x + 2)



C (x − 1)(x − 2)(x + 1)(x + 2)



D x(x − 1)(x − 2)

Answer 1

Answer with Step-by-step explanation:

The graph in the attachment has x-intercepts at

x=2,-2,1,-1

These are the solutions of the polynomial function represented by the given graph.

We can write all these solutions as factors to obtain,

x-2,x+2,x-1,x+1

The product of all these factors gives us the required function

(x-1)(x-2)(x+1)(x+2)

Hence, the correct option is:

C. (x − 1)(x − 2)(x + 1)(x + 2)

Answer 2

ANSWER

The function that the given graph corresponds to is

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



Step-by-step explanation

The given graph in the attachment has x-intercepts at


`image`


These are the solutions of the polynomial function represented by the given graph.




We can write all these solutions as factors to obtain,


`image`


The product of all these factors gives us the function whose graph was drawn.


This implies that,


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


Therefore the correct answer is option C.