Exponential Functions (CIE A Level Maths: Pure 3)

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Exponential Functions

Exponential functions

  • Exponential functions of the form y = ax with a > 0 are considered at A level

Exponential graphs

  • All graphs of the form y = ax will pass through (0, 1) because a0 = 1
  • The x-axis is an asymptoteExponential Functions fig1, A Level & AS Maths: Pure revision notes

a > 1

  • Where x < 0 the higher value of a is the “lower” graph
  • Where x > 0 the higher value of a is the “higher” graph
  • a > 1 is exponential growth (see Exponential Growth & Decay)

Exponential Functions fig3, A Level & AS Maths: Pure revision notes

0 < a < 1

  • Where x < 0 the higher value of a is the “lower” graph
  • Where x > 0 the higher value of a is the “higher” graph
  • 0 < a < 1 is exponential decay

6-1-1-notes-fig4

What about when a = 1?

  • You may like to think about why a = 1 is not considered... If a = 1, y = 1x = 1 for all values of x

Worked example

Exponential Functions Example fig1, A Level & AS Maths: Pure revision notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.