I have used
Show[Plot[x^2, {x, -10, 0}]
/. G_Line :> {Red, GeometricTransformation[G, TranslationTransform[{Sqrt[10], 0}]]}
/. L_Line :> {Red, GeometricTransformation[L, ScalingTransform[{1, 0.5}]]},
PlotRange -> {{0, Sqrt[10]}, {0, 5}}]
in Mathematica to plot
Please excuse my ignorance, but how would I find out the mathematics behind these vector transforms?
Important note:
I have cross posted this on Mathematica Stack Exchange also - please let me know if this is not accepted practice & I shall delete accordingly.