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.

Asymptotes revision resources to ace your exams

Learn more about asymptotes, trigonometric graphs, and types of graphs with our revision notes. To test your knowledge, try our exam questions about types of graphs.

For quick-fire GCSE maths revision use our collection of interactive flashcards for GCSE maths. We also have past papers for your exam practice.

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