How could I change an equation to look the same as it did with inverted axes?

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SUMMARY

The discussion centers on manipulating an equation to replicate its appearance when plotted with inverted axes in Mathematica. The user initially plotted the equation with x ranging from 1 to -1 and y from 1 to -1, achieving the desired visual outcome. To achieve the same effect with proper axes, the user seeks a method to adjust the equation by only replacing x with (-x) and y with (-y). Suggestions include exploring linear algebra techniques such as changing the basis.

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  • Experience with coordinate systems and axis manipulation
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Mathematics students, educators, and anyone using Mathematica for graphing who needs to understand how to manipulate equations for visual consistency across different axis orientations.

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How could I change an equation to look the same as it did with "inverted" axes?

I have graphed something in mathematica and when plotting I accidentally told it to plot the x and y axes backwards- as in x ranges from 1 to -1 from left to right and y ranges from 1 to -1 from bottom to top. Now the equation I was graphing looked exactly how I needed it to behave when plotting it with these incorrect axes.

If it possible to manipulate the equation some how so that when it is plotted with the proper axes it will look like the original equation did on the incorrect axes?

I have tried changing signs and inverting terms. Perhaps there is some linear algebra trick (changing basis or something?).

Any suggestions? Is this possible?
 
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Only replace x with (-x) and y with (-y); nothing else.
 

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