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# Surfaces

## Prompt

** “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.

## Context

This SWBQ probes students' notions about surfaces.

## Wrap Up

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).