how to specify domain of a function in wolfram alpha

Question

Is there a way to specify the domain for a function in wolfram alpha? I have a function which I want to plot. I want to restrict the function f(x,y) = xy(3-x-y) to x>=0, y>=3 and y <=3-x

Answer 1

Your restrictions make no sense. For x>=0 it follows that y<=3-x equals y<=3, but you also have y>=3, so this means that you want a plot for y=3. So, what you want to plot is apparently f(x)= -3x^2.

Other than that, I don't think WA currently allows a RegionFunction as in Mathematica

Answer 2

You can specify boundaries of the function parameters in Wolfram Alpha. They are more of a hint to the plotting library how much to scale the plot than exact boundaries, so in your case y is not calculated only with a value of 3. Although the boundaries in your case do not make much sense, as noted by @Sjoerd, this answer could be useful for setting sensible boundaries.

To plot your function, write the following in Wolfram Alpha: f(x,y) = xy(3-x-y) for x>=0, y=3..3-x

It works better with boundaries set around zero and univariate functions: plot y^2 cos(x), x=-6..6, y=-2..2 plot f(x) = -8/x + sqrt(7/x^2+1/x+1) for x=1..50

Reference: Wolfram Alpha Blog