# Thread: How to plot a 2 variable piecewise function in Mathematica

1. ## How to plot a 2 variable piecewise function in Mathematica

Hello I want to plot a sequence of functions (actually just the first few n, say for n=1,2,3).

Given an arbitrary function say a parabloid $\displaystyle f(x,y)=5-(x^2+y^2)$, how can a plot the first few values of the sequence defined below?

$\displaystyle f_n(x,y)=\left\{ \begin{array}{c} \left.\frac{k}{n},\text{if} f(x,y)\in \left[\frac{k}{n},\frac{k+1}{n}\right.\right), 0\leq k<n. \\ n, \text{if} f(x,y)>n\text{ } \end{array} \right.$

Something like a countour plot would be perfect if a 3d is hard to do.

2. Use the If command in Mathematica: If[condition, output if true, output if false]. Hint, though: Mathematica doesn't understand $\displaystyle 0\le k<n$, so you have to either use nested If statements, or use logical connectives (&&, I think) to get both conditions correct.

3. the $\displaystyle 0\leq k<n$ is just different values of the function on different intervals. so maybe multiple if statements are needed, or maybe a for loop. I've never written mathematica code before. but i'll try it out, thanks, some help on getting started would be appreciated. I'm not sure on how to define a function using an if statement.

i'm only used to seeing, g(x_, y_):=5-(x^2 + y^2) type definitions.