Graph all vertical and horizontal asymptotes of the rational function

Question

f(x)=x²+2x+1/x²-x-6

thank you in advance

Answer 1

You need to factor the denominator to find the vertical asymptotes. (x-3)(x+2). Where the denominator is equal to zero is where the vertical asymptote is. So you have vertical asymptotes at x = 3 and x = -2

You obtain the horizontal asymptotes from the ratios of the lead terms in the numerator and denominator. 1x²/1x². So the Horizontal is y=1. There are two other cases for horizontal asymptotes.

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