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IN PRE-CALCULUS ] Functions , Graphs , and Basic Mensuration Formulas

The first purpose of this article is to give a careful review of the concept of a function and its graph, and to give a proof of the fact that the graph of a linear function is a straight line. This fact is traditionally used in school mathematics without any explanation, but its proof holds the key to the understanding of the many forms of the equation of a straight line. A second purpose is to give careful proofs of all the standard area formulas of rectilinear plane figures, the point here being that the explanations of these formulas in most textbooks are incomplete. In the process, the meaning of the number π and the area formula of a circle will also be clarified. The article concludes with some general comments about volume, particularly the relationship between the volumes of generalized cylinders and cones which have the same base and the same height.