Asymptote

Asymptotes are formally defined using limits. The graph of the function approaches a value but will never reach it.

An example of asymptotes can be seen in the image below of the equation y = 1/x, in which two asymptotes are seen: the horizontal line y = 0 and the vertical line x = 0. In this example as the equation approaches the y-axis it will get increasingly small but will never reach zero. Think of the largest value you can and plug it in. 1 divided by your number will never reach zero.

On the other side, no matter how small of a number you plug in it will grow and grow and grow without an upper bounds. In each case the function approaches infinity as it apporaches the axis.