Which of the following graphs could be the graph of the function f(x) = x4 + x3 – x2 – x?

Asked by wiki @ 05/11/2020 in Mathematics viewed by 371 People

Answered by wiki @ 05/11/2020

Solution-

The given function is,

$f(x) = x^4+ x^3-x^2-x$

$= x^3(x+1)- x(x+1)$

$= (x+1)(x^3-x)$

$= (x+1)x(x^2-1)$

$= (x+1)x(x+1)(x-1)$

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

Therefore, at x=0, -1, 1 , f(x) will be 0 . Hence, 0, -1 ,1 are the x-intercepts.

Plotting the graph on desmos, the graph will be as in the attachment.

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Which of the following graphs could be the graph of the function f(x) = x4 + x3 – x2 – x?

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