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Exponential Functions (CIE A Level Maths: Pure 3)
Revision Note
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
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)
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
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
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