1. “Teach A Level Maths” Vol. 1: AS Core Modules
45: The graph of
© Christine Crisp

2. Module C2
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3. a is greater than 1. The function In this example, e.g.
Functions of this type, with a > 1, are called growth functions.
The reason for the name can be seen from the graph of

4. e.g.
Every time x increases by 1, the y value “grows” by doubling. e.g.

5. e.g.
Every time x increases by 1, the y value “grows” by doubling. e.g.

6. However far left we go, the graph never reaches the x-axis, even though it looks as though it does on a calculator or computer!
e.g.
Although is very small, it isn’t zero!

7. Tip: When sketching exaggerate the gap between the curve and the x-axis.
You don’t need to show the values on the x-axis. It’s the shape that’s important and the intercept on the y-axis.

8. Exercise
Sketch the graph of and, on the same axes, sketch the graph of
Solution
You can omit these

9. As the value of a increases in the graph gets steeper e.g.
All the curves pass through since for all values of a.

10. a need not be an integer e.g.
Also, if a = 1,

11. Instead of growing, the function decays
Values of a between 0 and 1
e.g. x x
Instead of growing, the function decays
e.g.
etc.

12. Exercise
Sketch the graph of and, on the same axes, sketch the graph of
Solution

13. Values of a between 0 and 1
e.g.
N.B. It is not possible for a to be less than zero.

14. a is never zero or negative .
SUMMARY
The function is defined for a > 0 and all values of x .
For a > 1, the function grows.
For ,the function decays.
All the curves pass through since for all values of a.
a is never zero or negative .

16. The following slide contains repeats of information on earlier slides, shown without colour, so that it can be printed and photocopied.

17. a is never zero or negative .
The function is defined for a > 0 and all values of x .
SUMMARY
For a > 1, the function grows.
a is never zero or negative .
For ,the function decays.
All the curves pass through since for all values of a.