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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)

Which function does this graph correspond to A xx 1x 1 B xx 1x 2x 1x 2 C x 1x 2x 1x 2 D xx 1x 2 class=

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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.

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)

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