An asymptote is an invisible line that a graph gets closer and closer to, but never, ever touches.

Think of it as an electric fence for your function. It's a boundary that the graph cannot cross.

There are two main types: Vertical and Horizontal.

A Vertical Asymptote occurs where the function is undefined, usually because of division by zero.

To find it, set the denominator of your rational function equal to zero and solve for x. That's your vertical asymptote.

A Horizontal Asymptote describes the behavior of the graph as x gets infinitely large or infinitely small.

To find it, you compare the 'degree' (the highest exponent) of the numerator and the denominator.

If the degree is bigger on the bottom, the HA is at y=0.

If the degrees are the same, the HA is the ratio of the leading coefficients.

If the degree is bigger on top, there is no horizontal asymptote (there might be a 'slant' asymptote instead).