Can you explain strange behaviour of a plot masked with $(2*(-1 + Abs[x]))/(-2 + Abs[Abs[-1 + x] - Abs[1 + x]])$?

Question

I made a code which draws a plot of $5-x^2$ masked with a kind of rectangular function in order to brake the branches of parabola at the points -1 and 1 and transform them into a vertical lines.

Clear["Global`*"]
rgbC = RGBColor[0.880722, 0.611041, 0.142051];
pltS = {rgbC};
f = 2 - Abs[Abs[-1 + x] - Abs[1 + x]]; 
(*triangular function with height 2 and base 2*)
lin = 2 - 
   Abs[2 x]; (*auxiliary function to make rectangular function of \
triangular function*)
k = FullSimplify[
   lin/f]; (*rectangular function with height 1 and base 2, defined \
on intervals x[-1,1] and y[1,-\[Infinity]]*)

eq1 = x^4;
eq2 = 5 - x^2 + k - 1;
fPlt = {Plot[I*x, {x, -2, 2}, AspectRatio -> Automatic, 
   PlotRange -> {{-2, 2}, {0, 
      5}}]}; (*empty 'canvas' for applicating combined mPlt and uPlt*)
\

mPlt = {Plot[{eq1}, {x, -3, 3}, Method -> "BoundaryOffset" -> False, 
   AspectRatio -> Automatic, Filling -> Top, 
   FillingStyle -> LightBlue, PlotRange -> {0, 3}]};
uPlt = {Plot[{eq2}, {x, -1.1, 1.1}, Method -> "BoundaryOffset" -> False, 
    PlotStyle -> {pltS}, PlotRange -> {{-2, 2}, {3, 5}}, 
    Filling -> Bottom, FillingStyle -> LightYellow]};

Show[fPlt, mPlt, uPlt]

The code works as expected when $x$ in uPlt varies from -1.1 to 1.1:

But things go curiouser when $x$ is bounded by -1 and 1, the vertical lines disappear:

And it all becomes curiouser and curiouser with $x$ is ranging from -2 to 2, now the only left "leg" is absent. The circumstances are aggravated by the error message 'infinite expression 1/0 encountered' popping:

Both legs are gowing back again with {x,-2,3} or {x,-3,3} and the error message persists. What is going on?

Answer 1

You should learn to cut out parts bit by bit until there is nothing left to cut that does not remove the problem. You can reduce the problem to this (the rest just obscures the problem):

Plot[eq2, {x, -1.1, 1.1}, Method -> "BoundaryOffset" -> False]

It comes from subtractive cancellation.

ClearAll[ff];
ff[x_?NumericQ] := Last@Sow[{x, eq2}];
uData = Plot[ff[x], {x, -1.1, 1.1}, Method -> "BoundaryOffset" -> False] // 
    Reap // Last // Last // Sort;

Just outside the domain, the round-off error leads to a denominator of 2.22045*10^-16 instead of zero. So what should be undefined results in a large, negative number that accounts for the vertical line going down:

uData[[41]]
(*  {-1.00034, -3.0354*10^12}  *)

eq2 /. x -> uData[[41, 1]]
(*  -3.0354*10^12  *)

(The sampling of Plot is slightly asymmetric, which results in graphs with asymmetries that are usually negligible. But not in the OP's cases.)

P.S. You can track down the round-off error with

uData[[41, 1]];
eq2 /. x -> % // Trace

P.P.S One thing that usually fixes round-off error is a higher WorkingPrecision:

Plot[eq2, {x, a, b},..., WorkingPrecision -> 16]

This works on the three cases in the OP.