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Weekly Challenge 43: A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

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Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

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Weekly Challenge 28: the Right Volume

Can you rotate a curve to make a volume of 1?

Weekly Challenge 5: Trigger

Stage: 5 Short Challenge Level: Challenge Level:1

To sketch any graph look for:
 
zeros;
 
turning points;
 
asymptotes;
 
positive values and negative values;
 
the evaluation of the function at key points, such as $0$, $\pm 1$ or the boundaries of the range or domain of the function (i.e. the possible input values and max/min output values).
 
Also, ask yourself: Does the graph vary smoothly from point to point?