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

Solution-

The given function is,

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.

The function cuts the x-axis at 0, 1, and -1. The function is a 4-degree polynomial whose graph is attached to the image.

Given:

The given function is .

It is required to draw the graph of the function.

First, factorize the given function as,

So, the function will cut the x-axis at 0, 1, and -1. For values less than -1, the graph is positive and decreasing. For values between -1 and 0, the graph is positive and increasing-decreasing. For values between 0 and 1, the graph is negative and decreasing-increasing. Finally, for more than 1, the function is positive and increasing.

The graph of the function is attached to the image.

Therefore, the function is a 4-degree polynomial whose graph is attached to the image.

For more details, refer to the link:

link

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