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Introduction
Being a somewhat geeky Maths ‘nerd’, I spent days leading up to Valentine’s day trying to find a Maths function appropriate to the day. In the end, I did not find an appropriate single function but (perhaps aptly enough) a pair: function and inverse function. It occurred to me that these provide a good opportunity to illustrate a number of simple mathematical transformations involving reflections in the x-axis, y-axis, and both x-axis and y-axis. Whilst the inverse function itself illustrates reflection in the line y=x.
The Function (and its Inverse)
So here is the pair of graphs I initially settled upon: $$y=-x(x-4)$$ and $$x=-y(y-4).$$ As can be seen, there is some semblance of a heart shape formed by the function and its inverse. Perhaps not quite what Valentine card designers would be looking for!
It intrigued me to note that this particular function and its inverse have 4 points...
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