Asymptotes - GCSE Maths Definition

What are asymptotes?

In GCSE maths, asymptotes are lines which a curve approaches, but does not cross. A simple example is the graph of y=1/x. As the value of x increases, the value of y decreases, but will never reach zero. Therefore, there is a horizontal asymptote at y=0.

The graph of y=1/x also has a vertical asymptote at x=0. This is because as x gets very small (close to zero), y becomes very large. 

y=1/x does not have a value at x=0, as dividing by zero is undefined; i.e., it has no value. Therefore the curve never crosses the line x=0, so there will be an asymptote at x=0.

What other graphs have an asymptote?

Another example of asymptotes is seen in the graph of y=tan x.This trigonometric function features vertical asymptotes every 180 degrees, starting at 90. This means there are vertical asymptotes at x=90, x=270, x=450, and so on. You can find out more about trigonometric graphs in our revision notes.