1. How do we know if a graph has a horizontal asymptote? What are the three options?
We know if a graph has a horizontal asymptote when we compare the degrees of the numerator and the denominator. If there is a bigger degree on the bottom, then the asymptote is y=0. If the numerator and the denominator have the same degree, then the asymptote is the ratio of the coefficients. If there is a bigger degree on top, then there is no horizontal asymptotes. The equation is y=0. The limit notation is as x approaches positive infinity, f(x) approaches a number and as x approaches negative infinity, f(x) approaches a number.
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