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Exponential functions have the form y = aˣ, including the special case y = eˣ whose gradient equals its value. This topic covers the shape and key features of exponential graphs and transformations of eˣ. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Every exponential curve passes through 0, 1 and approaches the x-axis without touching it. A larger base grows faster; a negative exponent reflects it. Transformations follow the usual rules, moving the asymptote with them.
Before you start
Bring index laws and graph shapes with you. It underpins logarithms and modelling. It belongs to the Pure 2 specification.
What you learn
That one change — variable in the exponent, not the base — gives a graph with a very particular shape, and it's the shape behind almost every real model of growth and decay. The course works through what an exponential function looks like, growth, decay and bases below 1, vertical shifts and stretches — the moving asymptote, reflections, horizontal shifts and combinations and modelling growth and decay. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our A-level maths courses, Exponential Functions & Graphs belongs to Exponentials & Logarithms and is met in the AS year. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Related topics students usually take next include Exponential Growth & Decay, Introducing Logarithms, Laws of Logarithms and Logarithmic Graphs (Linear Form). For unlimited practice, the Exponentials & Logarithms revision engine builds new questions on demand and records your accuracy.
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