Rational function in mathematics teaching

U ovom diplomskom radu obrađena je racionalna funkcija u nastavi matematike. To je elementarna funkcija koja je dio kurikula za nastavni predmet matematika u srednjoj školi, ali pomalo zapostavljena u nastavi. Obrađen je pojam racionalne funkcije te njena svojstva počevši od obrnute proporcionalnosti do funkcije s kvadratnim izrazom u brojniku i nazivniku. Posebno je istražen utjecaj koeficijenata na graf pripadne funkcije te su izrađeni metodički materijali pomoću kojih učenici mogu samostalno, ali i uz pomoć programa dinamične geometrije, istraživati svojstva racionalnih funkcija. Na kraju, dan je projektni zadatak koji objedinjuje sve spoznaje o svojstvima racionalne funkcije, ali i prikazuje primjenu iste u medicini.In this master’s thesis, the rational function in the teaching of mathematics is treated. It is the elementary function that is part of the curriculum for the subject of mathematics in high school, however it is somewhat neglected in teaching. The notion of a rational function and its properties are processed, starting from inverse proportionality to a function with a square expression in a denominator. The influence of coefficients on the graph of the corresponding function was especially investigated, and methodological materials were developed with which students can independently, but also with the help of dynamic geometry programs, investigate the properties of a rational function. Finally, a project task is given that brings together all the knowledge about the properties of a rational function, but also shows the application of the same in medicine