1. How do we know if a graph has a horizontal asymptote? What are the three options?
Graphs have many parts to them as you can see from the photo to the right. The horizontal asymptote is the line that goes straight across the y-axis(the pink line). You know if a graph has a horizontal asymptote when there is a bigger degree on the bottom which makes the asymptote y=0. If the numerator and denominator have exponents with the same degree, then the asymptote is basically the leading coefficient of the numerator over the leading coefficient of the denominator. On the other hand, there will be a case in which you will NOT have have a horizontal asymptote which is when there is a larger degree of the exponent on top.
Note that graphs can occasionally cross through the middle of a horizontal asymptote; however, NEVER toward the ends of the line (meaning far left or far right). Also, you can only either have a horizontal asymptote or a slant asymptote in a graph, NEVER both.
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