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Witch of Agnesi
Age 16 to 18
Challenge Level 
Consider symmetry.
Find the critical values (turning points).
Consider what happens to the graphs for large $x$ (possitive and negative) and hence find the asymptote.
Find the critical values (turning points).
Consider what happens to the graphs for large $x$ (possitive and negative) and hence find the asymptote.
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Power Up
Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x