The image in the warm-up shows one of a family of functions represented by the implicit equation \((x^2+2ay-a^2)^2=y^2(a^2-x^2)\).

Try changing \(a\) using the slider in the applet below.

What do you notice about other functions in the family?

Can you use a combination of the information provided by the graphical and algebraic representations to answer and explain some of the questions below?

- What is special about the points:
- \(x=a\)
- \(x=-a\)
- \(x=0\)

Will each member of the family be represented by two curves? Why?

What is the domain and range of each member of the family?