# Find the parameter region where function returns negative value

I have a function $$f(m,n)$$ where m and n are positive integers. Suppose $$f(m,n)$$ is like a black box, I can get values of it when I enter values of m and n. I want to scan over a region for example $$4 to find where $$f(m,n)<0$$. Then make a plot of the region where it satisfies the requirement.

For the plot part, I think I can directly use the Listplot if I can successfully generate a parameter list for m and n where $$f(m,n)<0$$. For the first part, I could use the command For to generate the list satisfying the requirement. I guess this is not the most ideal command I want to use in Mathematica.

• So if you have something like this with 9025 randomly positive and negative points would you be interested in defining positive/negative parametric regions, shown in two colors?
– Syed
May 10, 2022 at 15:57

RegionPlot[Sin[x]^y - 10 < 0, {x, 0, 1000}, {y, 0, 1000}] displays
• @Vayne You only have to substitude Sin[x]^y - 10  by your mystical f[x,y]  in @Romanp 's nice answer and it should work! May 10, 2022 at 15:26