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

The function that the given graph corresponds to is
[tex]f(x) = (x - 2)(x - 1)(x + 1)(x + 2)[/tex]



EXPLANATION

The given graph in the attachment has x-intercepts at

[tex]x = - 2
,x=-1,x=1 \: \: and \: \: x=2[/tex]


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




We can write all these solutions as factors to obtain,

[tex]x + 2
,x + 1 ,x - 1 \: \:and \: \: x - 2 [/tex]


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


This implies that,

[tex]f(x) = (x - 2)(x - 1)(x + 1)(x + 2)[/tex]


Therefore the correct answer is option C.