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## 'Rational Request' printed from http://nrich.maths.org/

For a secret reason, my friend wants a curve which has 4 vertical
asymptotes and 3 turning points.

Could you sketch him such a curve? Could you find an algebraic form
for such a curve? Could you find many different curves with such
properties?

My other friend wants a curve which also has 4 vertical asymptotes,
but only 2 turning points. Can her needs be met algebraically?

As you consider this problem, many
questions might emerge in your mind such as: "what makes one type
of curve 'the same' as or 'different' from another?" or
"can I satisfy requests for other numbers of asymptotes and turning
points?". Why not make a note of these questions and ask your
teacher, yourself or your friends to try to solve them?