What is an asymptote?
An asymptote is a limit on a function so that the function will never touch the line at the asymptote, but will get infinitely close.
I'll use this section for examples and extra explaining.
Take the function
We know that
#x != -4#as if it were the function would be undefined. This is an asymptote in the graph.
Basically it is an invisible line that the graph cannot touch no matter what. However, the function can appear on the other side (as seen in the above equation).
An asymptote can be found by evaluating what makes the denominator = 0. In the above function it is -4. We also need to make sure that those values that make the denominator = 0 do not make the numerator = 0, as those would be holes in the graph, which are different.
Hope this helped!