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Function recognition and functional notation

96     FncValue     The problem of evaluating these expressions becomes trivial, once the concept of functional notation is understood. The problem involving a radical does underscore the advantage of taking the roots of the factors of a product when possible (i.e. take the roots before multiplying).

97     FncGraph     These problems provide a very good exercise in understanding the meaning of functional notation and in identifying the family of a function from a few points of its graph. The student should make a rough sketch of the graph described by the functional notation.  If the function is properly identified, the student is asked to give the value of the function at two points from the corresponding graph.  The screen indicates that the tolerance for reading the graph points is ±  0.5.  Actually the tolerance becomes even larger for rational functions, where the curve rapidly gets very steep. If it looks as if the required point may be undefined (as at the discontinuity of a rational function), then the student should input {U} for undefined. Otherwise, an attempt should be made to estimate to the nearest  0.1 unit.

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