AS/A2 Pure 4 Pure 6

P5 Topic 2: Hyperbolic functions
Graphs and properties: coth ax
Change the value of a and describe the geometric symmetry of the curve.

Summary coth ax is an example of an odd function, ie., f(-x) = -f(x) The curve has rotational symmetry about the origin The curve has an asymptote at x=0 coth ax £ -1 or coth ax ³ 1 for all values of a or x Based on free Java applets from JavaMath