AS/A2 Pure 1 Pure 3

P2 Topic 2: Functions
y=axn
Investigate the effect on the shape of the graph of changing a and n. Pay particular attention to the integer values of n, ie., n = 1, 2, 3 and 4. Which of these are even functions and which are odd?

Summary All even functions have mirror symmetry about the y-axis. All odd functions have rotational symmetry about the origin. Therefore y=x and y=x3 are odd, whereas y=x2 and y=x4 are even. Extension activity: Investigate y=xx and the value of 00 A note about graphic calculators A graphic calculator may be allowed in your exam. The TI-83, or similar model, can display these graphs for you. Select the Y= screen: Enter Y1 = A^X Then select the GRAPH screen. You can then choose different values for the constant A. For example, to make A = 1, press 1 ALPHA A. You are not "programming" your calculator when you do this, so there should be no problem with setting up your calculator in this way before entering the examination hall, but you ought to check this first. Based on free Java applets from JavaMath