AQA A Level Maths: Pure复习笔记6.1.1 Exponential Functions

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 asymptote
  • 6.1.1-Exponential-Functions-fig1

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)

6.1.1-Exponential-Functions-fig3

0 < a < 1

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

6.1.1-Exponential-Functions-Example-fig1

 

 

 

 

 

 

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