The place of the elementary calculus in the senior high-school mathematics : and suggestions for a modern presentation of the subject . mbol given for its representation,nevertheless the meaning of a function has been developed to a con-siderable The idea of functional relationship is containedin much of the preceding mathematics, and the pupils are preparedfor further instruction in the function idea even if it had not beenexplicitly commented upon heretofore. Illustration of the Function Idea. The pupils plot the specific curvey = x2 — + 5- This recalls to the pupils the ideas t
The place of the elementary calculus in the senior high-school mathematics : and suggestions for a modern presentation of the subject . mbol given for its representation,nevertheless the meaning of a function has been developed to a con-siderable The idea of functional relationship is containedin much of the preceding mathematics, and the pupils are preparedfor further instruction in the function idea even if it had not beenexplicitly commented upon heretofore. Illustration of the Function Idea. The pupils plot the specific curvey = x2 — + 5- This recalls to the pupils the ideas they havelearned about graphs, and bringsthem up to a point where theirminds are prepared to receive thenew ideas. Then, guided by the teacher,they select some suitable point Pon the curve and draw the ordi-nate PM. It is seen that the valueof the expression y = x2 — 4X + 5at the point P is the length of theordinate PM. This is an impor-tant relation that is used later inthe explanation of the derivative. The expression y -2 _ 4*+ 5 may be read y is an expressioncontaining x. However, in thelanguage of the calculus, instead of. Scale:lunft= 2 spaces Fig. 10 6 Secondary School Circular, United States Bureau of Education, No. 5, February,1920. The ideas on the function concept contained in this circular are expanded uponand it is shown in detail how they may be applied in the classroom in the treatment ofspecific topics, in a report by The National Committee on Mathematical Requirements,February, 1921. 54 Elementary Calculus in Senior High-School Mathematics saying an expression containing x, it is read y is a function of xThe symbol for a function of x is / (x) and is read function of in the language of the calculus y — x2 — + 5 would bewritten f (x) = x2 — + 5. This is read a function of x isx2 — 4X -f- 5. Hence here y and/ (x) stand for the same thing, thatis, y is identical with/ (x). Since 3; represents the length of the ordinateat some point P, the
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