Level Sets

A set of $\mathbb{R}$-valued functions that only takes a given constant $c$ to represent 3D Graphs.

Formal Definition

Given a value $c$, the level set is: $L_c=\{x\in D:f(x)=c\}\subset {\mathbb{R}}^n$

• If $n=2$, then this set is a level curve
• If $n=3$, then this set is a level surface

Example

Find level sets $L_c$ of $c=4$ for the function $f(x,y)=x^2+y^2:D={\mathbb{R}}^n$ $L_4=\{(x,y)\in {\mathbb{R}}^2|x^2+y^2=4\}$ Note that this is a circle of radius $2$ and center $(0,0)$