Level Sets & Contour Points
Text The collection of all points x in the domain of a function f for which f(x) = c is called the level set of f at level c.
The level set of f is empty if there is no point x in the domain of f for which f(x) = c.
In general the contour of a funcion f of one real variable will be a finite set of points in the domain.
Demos
Contour Points
 
This demo shows the contour points of a function f(x), colored according to the value of f(x). Points that have the same color are part of the same level set.

Exercises 1. Find the points in the level set for each of the following:
 f(x) = x, c = 0
 f(x) = x^{2}  1, c = 0
 f(x) = sin(x), c = √2/2
 f(x) = tan(x), c = 1
2. Given a function f(x) with level set A at c = 0 and a function g(x) with level set B at c = 0, what is the level set of the function fg(x) (equal to f(x) * g(x)) at c = 0?
