Unit G Summary Question #1: Horizontal Asymptotes

How do we know if a graph has a horizontal asymptote? What are the three options?

To answer this question, first I feel the need to define what a horizontal asymptote is. A horizontal asymptote is an imaginary horizontal line that a graph cannot touch like in the example above where that curved line got close to but did not cross the y=4 horizontal asymptote. We know if a graph has a horizontal asymptote when we see that a graph approaches a y-value but never actually reaches it in a graphing calculator or in a graph in general. Another way we know if a graph has a horizontal asymptote is when you find that you get a bigger degree on the bottom (the denominator) after you compare the degrees of the numerator and the denominator of a function. The third way is when both the numerator and denominator of a function have the same degrees.