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

2. "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" Module C2

3. 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 In this example, a is greater than 1. The function

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

5. Every time x increases by 1, the y value “grows” by doubling. e.g. 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. Sketch the graph of and, on the same axes, sketch the graph of Solution You can omit these Exercise

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 e.g. etc. Values of a between 0 and 1 x x

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.  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.

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

17.  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.