Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2018 / Paper 1 / 14 / a

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Solution

The exponential function is strictly positive, so the zero level set is determined entirely by its prefactor:

x y = \frac{1}{4}, equivalently y = \frac{1}{4 x} (x \neq = 0) .

This is a rectangular hyperbola with branches in the first and third quadrants.

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