AS/A2 Pure 1 Pure 3

P2 Topic 2: Functions
Odd and even functions
Functions with the property that f(-a) = f(a) for all values of a are called even. Functions with the property that f(-a) = -f(a) for all values of a are called odd. Decide for each of the Curves 1 to 10 given below, whether they are odd or even or neither. What geometric properties do odd and even functions have?

Summary Curve 1: even Curve 2: odd Curve 3: even Curve 4: neither Curve 5: even Curve 6: even Curve 7: odd Curve 8: neither Curve 9: odd Curve 10: odd All even functions have mirror symmetry about the y-axis. All odd functions have rotational symmetry about the origin. Based on free Java applets from JavaMath