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In the following, a few functions are to be analysed with as little help of technology as possible. We assume we have no tool to plot implicit relations -so no Mathematica, TI Nspire, Geogebra or similar. The graphs are finally done using these tools though.

We will start with three similarly-looking relations – even if the graphs are quite different.

(Note for IB MAHL students. You are not supposed to do this thorough analysis in an exam question, even if many elements may occur. Using implicit derivatives to find slopes and min/max of implicit relations is a part of the syllabus, but finding *dx/dy* is not. Finding asymptotes, yes, but finding asymptotes that are not linear relations, no – even if it might be useful at times. Tip: A thorough analysis of some relations like these might be a maths exploration.)

- The relation y^3+y^2=x^3+x^2
- The relation y^3+y^2=x^2+x
- The relation y^3+y^2=(x^4)y+x^2
- The relation y^3+x^2=y/x

Up a level : Calculus and Analysis

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