AS/A2 Pure 4 Pure 6

P5 Topic 2: Hyperbolic functions
Graphs and properties: arctanh(ax) and logs
Move the point a left or right to change the value of the parameter a in the graphs of y = arctanh(ax) and y = ½ln[(1+ax)/(1-ax)]. What do you notice?

y = arctanh(ax)	y = ½ln[(1+ax)/(1-ax)]

Summary clearly arctanh(ax) = ½ ln[(1+ax)/(1-ax)] The Plane Graphic Calculator java applet