# Create a RegionPlot with an inequality over an intervall of a variable?

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 Tobias Frohoff 1 Vote Hello community, I'm new here and also a beginner in mathematica.I want to do an RegionPlot in mathematica, but my provided inequality should hold over an intervall of a third variable. An example of my problem: f[x_, y_, z_] = x + y*z; RegionPlot[f[x, y, z] > 0, {x, -2, 2}, {y, -2, 2} for {z, -0.5, 0.5}] Sorry, I know that it is not possible in this way however I hope that someone understand what I want to do.Thank You for answering!
 Sander Huisman 2 Votes In general this can be very tricky, as you have to calculate what (I believe) is called an envelope. However you problem is not completely specified. Do you want to the inequality to hold for ALL z, or for SOME z? Depending on this the answer is different. Since you're function is easy one can just evaluate the end-points of 'z' and use logical operations on that: f[x_, y_, z_] := x + y*z; RegionPlot[f[x, y, 0.5] > 0 \[And] f[x, y, -0.5] > 0, {x, -2, 2}, {y, -2, 2}] RegionPlot[f[x, y, 0.5] > 0 \[Or] f[x, y, -0.5] > 0, {x, -2, 2}, {y, -2, 2}] 
 Sander Huisman 2 Votes For more difficult cases one can make a helper function that will check if a point belongs to a region or not. Here is a simple function that tries to do it numerically: ClearAll[Envelope] Envelope[f_, x_?NumericQ, y_?NumericQ, {a_?NumericQ, b_?NumericQ, n_Integer: 100}, comb_: Or] := comb @@ Table[f[x, y, z] > 0, {z, Subdivide[a, b, n]}] f[x_, y_, z_] := x + z y + Sin[6 z]; Quiet@RegionPlot[Envelope[f, x, y, {-0.5, 0.5}], {x, -2, 2}, {y, -2, 2}] Quiet@RegionPlot[Envelope[f, x, y, {-0.5, 0.5}, And], {x, -2, 2}, {y, -2, 2}] For this function one can not simply take the end points as the function is not monotonically increasing. This function will take several points of z and check if they belong to the set, and then using either OR or AND decide what to do.