# Possible bug with RegionPlot

RegionPlot[ImplicitRegion[(2 x - 1)/(x - 1) < 3/2, {x, y}],
PlotRange -> {{-9, 9}, {-9, 9}}]


Just checking whether anyone else can replicate this. Can anybody confirm such behavior and, maybe, confirm this as a bug?

• Same result with Linux 11.0.1 – grbl Feb 8 '17 at 8:34
• It does not work on 10.4.1 too. The following inequalities also do not work: 1/x < 1 and 1/x <-1. – Anjan Kumar Feb 8 '17 at 8:50
• Yes, I think that's a bug and it would be good if you could report it. – user21 Feb 8 '17 at 9:50
• The bug is still present in 11.1.0 – user58955 Mar 23 '17 at 17:50

Another thing to do is just cut ImplicitRegion out of the loop altogether. RegionPlot is naturally designed to take a predicate of inequalities.

RegionPlot[(2 x - 1)/(x - 1) < 3/2, {x, -9, 9}, {y, -9, 9}]


There have been other examples of RegionPlot having trouble with ImplicitRegion, and usually the answer is just to give the inequalities to RegionPlot directly.

• much simpler (and natural) +1. Hope WA is going well – ubpdqn Feb 9 '17 at 0:39

This can worked around by using Reduce,e.g:

p = Plot[(2 x - 1)/(x - 1), {x, -5, 5},
GridLines -> {{-1, 1}, {3/2, {2, Red}}}, PlotRange -> {-5, 5},
Frame -> True];
rp = RegionPlot[
ImplicitRegion[Reduce[(2 x - 1)/(x - 1) < 3/2, x], {x, y}],
PlotRange -> {{-9, 9}, {-9, 9}}, PlotStyle -> {Pink, Opacity[0.2]}];
Show[p, rp]