Surfaces

“How many ways can you represent a function of several variables?”

Simpler prompts such as “What is a surface?” are not as effective because they lead students to use non-mathematical language.

This SWBQ probes students' notions about surfaces.

Work with students to create as long a list as possible of representations of functions of several variables. Possible representations include:

• graphs (surfaces);
• tables;
• equations ($x^2+y^2+z^2=4$);
• functions ($f(x,y)=x^2+y^2$);
• level sets (contour maps);
• geometric objects (spheres).