Discussion on the Three Quotations Related to the Definition of Function in the Textbook by People’s Education Press (Edition A)

An analysis is given to the three quotations concerning the definition of function in the textbook published by People’s Education Press (Edition A) .The three quotations involve background knowledge like projectile motion, ozone layer and Engel coefficient, etc., the lack of sufficient knowledge of which would result in their difficulty in understanding.When introducing the concept of function, the students are apt to confuse the concept of“quantity”and“number”, to mistake quantity set (whose elements are quantities) for number set, or mistake a mapping for a function.In teaching, in general, from the mapping to the function, the change should be displayed as the process of abstraction.A teaching suggestion that mathematical operation be used as the introductory step for the learning of the functional definition is put forth.It points out the essence of the special correspondence relation of function—each value of the independent variable in the domain shall correspond to one and only one function value.And counter examples are quoted to strengthen the understanding of the function definition.