1. What do you notice about the graph of the function when b is less than one(specifically between zero and 1)? What about when b increases to values greater than one?
2. Why can't b=0 or a number less than 0?
3. What happens when b=1?
After showing the first point:
1. When does the log_b(a) equal a negative value? Try this for both b-values less than one, and then for b-values greater than 1.
2.When does the function cross the x-axis? Is this true for all values of b? Why?
After showing both points:
1. When do the two points have the same coordinates? Why?
2. Hold b constant and change a. What shape does the second point trace?
3. Now hold a constant and change b. What shape does the second point trace? Why is this true?

Jessica Bartlett, 25 November 2013, Created with GeoGebra