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 [tex]f(x) = x^4 +x^3-x^2-x[/tex].
It is required to draw the graph of the function.
First, factorize the given function as,
[tex]f(x) = x^4 +x^3-x^2-x\\f(x)=x(x^3+x^2-x-1)\\f(x)=x(x^2(x-1)+2x(x-1)+1(x-1))\\f(x)=x(x-1)(x^2+2x+1)\\f(x)=x(x-1)(x+1)^2[/tex]
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.
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https://brainly.com/question/24630184
