Question 173228
For both logarithmic and exponential functions, you might want to discuss the curve asymptotes and where the curves intersect one or the other of the axes.  What happens as x increases in a positive direction?  What happens as x decreases (in a negative direction for the exponential function, and as x gets close to zero for the logarithmic function)


You should also make mention of the fact that there is something very interesting about where exponential functions cross the y-axis and where logarithmic functions cross the x-axis.  I'll let you discover exactly what this interesting thing is for yourself.


Are these functions always increasing as x increases?  Always decreasing?  Or are there local maxima or minima?


Another interesting thing you might do is to sketch a graph of {{{y=a^x}}}, {{{y=log(a,(x))}}} (picking some convenient value for {{{a}}}, but making sure it is the same value for both functions), and the line {{{y=x}}}, all on the same piece of graph paper.  Then fold the paper along the {{{y=x}}} line and hold the paper up to the light.


In addition to the purplemath site your instructor suggested, Wikipedia has excellent articles about exponential and logarithmic functions.  You might also try Cliff's Notes and Wolfram's Math World.


Good luck.