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Math·Advanced Math·Nonlinear functions

hard

The function $y=g(x)$ is graphed in the $xy$-plane above. Which of the following equations could describe $g(x)$?

A

$g(x)=(x+1)(x+2)(x-4{)}^2$

B

$g(x)=-(x-1{)}^2(x-2)(x-4)$

C

$g(x)=(x-1{)}^2(x-2)(x+4)$

D

$g(x)=(x+1{)}^2(x+2)(x+4)$