Thread: Help Graphing a Polynomial

How do I graph this Polynomial?
I need to also show the asymptotes and hole(s).

F(x)= (-(x^4)-(3x^3)-7x-21) / ((x^3)-(7x^2)-5x-75)

Originally Posted by Kairo

How do I graph this Polynomial?
I need to also show the asymptotes and hole(s).

F(x)= (-(x^4)-(3x^3)-7x-21) / ((x^3)-(7x^2)-5x-75)

If you can factor a polynomial from both numerator and denominator, there will be a hole in the graph. If when you factor nothing cancels, the real roots of the denominator will have vertical asymptotes.

Since the numerator has a higher power, you will have a slant asymptote. You can solve that by long division; furthermore, the SA will be the solution to the division disregarding any remainders.

The first thing you should know is that this is not a polynomial! It is a "rational function". Asymptotes occur where the denominator is 0 but the numerator isn't. "Holes" occur where both numerator and denominator are 0.

Originally Posted by HallsofIvy

The first thing you should know is that this is not a polynomial! It is a "rational function". Asymptotes occur where the denominator is 0 but the numerator isn't. "Holes" occur where both numerator and denominator are 0.

I never said the function as a whole was a polynomial. If we look at the numerator and denominator independently, we have two polynomials. If those polynomials happen to factor to a form of (x-2)(...)/(x-2)(!!!), then where ever the factors cancel there will be hole in the graph. Sorry for no latex but I am on my phone.