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I'm a maths teacher and today was having a discussion with my Head of Department about asymptotes (as you do!)

She was me if I could think on an equation of a graph(s) which has an asymptotes at the line y=x and another at y=-x.

Thinking about it, neither of us could come up with anything. It's really bugging me now. I ain't too sure if there is such a function...though it seems silly there not being.

The only way I managed to get a graph like what I wanted was to rotate the graph of y=1/x by various angles.

So can such a graph exist? Is it possible to transform equations of graphs via rotations (something I can't ever remember doing)?

Hope I can come up with an answer by tomorrow :)