Why do this problem?
The problem gives practice in the usual techniques for cuve
sketching (considering symmetry, finding turning points, looking
for asymptotes). It also introduces the idea of a family of
Suggest different members of the class sketch the different graphs
(for $a=1$, $2$ and $3$). Have a class discussion about the results
Will the graphs have a similar shape for all values of $a$?
What about negative values of $a$?
If the class can differentiate simple functions defined
parametrically or implicitly then they could also try:
Folium of Descartes .