Abstract
1. (1) The conditions under which plots of y versus ( y x ) can be concave downwards or concave upwards is fully discussed together with some new methods for analysing complex plots given by high degree equations. 2. (2) The approach is to analyse rational polynomial functions of the type y = P n Q m (i.e. n: m in the degree of independent variable x) in the implicit form F(y, y x ) = 0 for intercepts and local gradients and concavities as x → 0 and x → ∞. 3. (3) It is shown that the 2:2 y versus x → 0 x function gives y versus ( y x ) plots which are conic sections and the conditions determining the family to which any given function will belong are stated. 4. (4) The 3:3 function is also discussed and some examples are given.
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