How to find the vertical & horizontal asymptotes of a rational function? (4 examples)

How do we find the vertical asymptotes and horizontal asymptotes of rational functions? Remember for a vertical asymptote of a rational function, we must set the denominator equal to 0 *after* we have reduced the rational function (but if the question is asking for the domain of a rational function, then we must set the denominator equal to 0 in the original rational function). For the horizontal asymptotes of rational functions, just compare the highest power of x on the numerator and the highest power of the denominator.

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[ArtemisPlaysGamez]

7:17 for the function f(x) =(x^2)/(x+1), the degree of the polynominal on top is 2 and the bottom is 1, and there are no horizontal asymptotes. however, if you plot it in desmos, the graph does not cover -4=<y=<0 meaning there are several asymptotes.. ?? explain pls