Question

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

Answer 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 attachme

Explanation:

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)