Philippine E-Journals

Mathematical Investigation of Functions

Rene V. Torres

Discipline: Education

 

Abstract:

Generally, when the independent variable of a given exponential function is used as an exponent, the function is considered an exponential. Thus, the following can be examples of exponential functions: f(x)=abx+c, f(x)=aebx+c + c, or f(x) = ea2+bx+c. However, deriving functions of these types given the set of ordered pairs is difficult. This study was conducted to derive formulas for the arbitrary constants a ,b, and c of the exponential function f(x)=abx+c. It applied the inductive method by using definitions of functions to derive the arbitrary constants from the patterns produced. The findings of the study were: a) For linear, given the table of ordered pairs, equal differences in x produce equal first differences in y y; b) for quadratic, given the table of ordered pairs, equal differences in x produce equal second differences in y; and c) for an exponential function, given a table of ordered pairs, equal differences in x produce a common ratio in the first differences in y. The study obtained the following forms: b=d√r, a=q/b⋅n(bd−1), c=p-abn. Since most models developed used the concept of linear and multiple regressions, it is recommended that pattern analysis be used specifically when data are expressed in terms of ordered pairs.