Plot the graph of x^y = y^x in the first quadrant and explain its
Stage: 5 Challenge Level:
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
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?
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.