Exercises - Implicit and Parametric Functions

First we will identify sets given by implicit relations. The next batch of problems concerns expressing parametric curves as implicit or explicit functions and identifying their shapes. Then we do problems on sketching graphs of parametric curves.

If you want to refer to sections of Methods Survey on implicit and parametric functions while working the exercises, you can click here and it will appear in a separate full-size window. Similarly, here we offer Theory.

 

Identify sets given by the following implicit relations. Make a sketch if possible.

Express the following parametric curves either as functions y = y(x) or as implicit curves F(x,y) = k, identify their shapes and sketch them.

Sketch the graphs of the following parametric curves using the standard algorithm.

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