Question

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

Answer 1

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.

Answer 2

Answer:

A, or the first graph. :)

Step-by-step explanation: