A Discontinuous Function

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In[1]:=

   Clear[z]; 
  z = 1/(x y); 
    xRange={x,-4,4};yRange={y,-4,4};

In[2]:=

  cp1 = ContourPlot[z,Evaluate[xRange],Evaluate[yRange]];

In[3]:=

  cp2 = Show[cp1,ContourShading->False];

In[4]:=

  dp1 = DensityPlot[z,Evaluate[xRange],Evaluate[yRange],
        PlotPoints-> 50, Mesh -> False];

In[5]:=

  Here I added a contour plot with a larger number of
  plotpoints, the same as the previous picture.

In[6]:=

  cp2 = Show[ContourGraphics[%]];

In[7]:=

  Show[SurfaceGraphics[%],Mesh->False];