# Visualization of a function in which the range of values and functions change

I have this function I want to visualize this function，So I use this

data = Table[{b, #, (b + #)/(b^2 + #)}, {b, 1/5, 5*#}] & /@
Range[0.3, 0.8, 0.001];
Flatten[data, 1] // Point // Graphics3D


get this This image is very strange and it doesn't feel like what I wanted

Your approach is alright but you need the ListPlot3D function.You need to check documentation properly 🙂.

data = Table[{b, #, (b + #)/(b^2 + #)}, {b, 1/5, 5*#}]& /@ Range[0.3, 0.8, 0.001];
ListPlot3D[Flatten[data, 1]]


But you can allow mathematica to do the heavy lifting. Let's define your simple and bounded 2D region like this.

reg = ImplicitRegion[1/2 < b <= 5 c && 0.3 < c < 0.8, {b, c}];
RegionPlot[reg, PlotRange -> All] Now get a continuous 3D plot of the surface of interest.

Plot3D[(b + c)/(b^2 + c), {b, c} \[Element] reg] It is also possible to get the surface without defining the region but using the RegionFunction option of Plot3D like this.

Plot3D[(b + c)/(b^2 + c), {b, 1/2, 4.5}, {c, 0.25, 0.85},
RegionFunction -> Function[{b, c, z}, 1/2 < b <= 5 c && 0.3 < c < 0.8]]