Abstract:

Understanding the notion of function and various types of basic functions is a key skill of students in more advanced courses not only in mathematics but also in subjects such as physics, economics, sociology and technology in general. It is mainly the use of trigonometric functions - oscillation, acoustics - and logarithmic and exponential functions - population growth or decline, interest rate, radioactive decay etc.

Students come from secondary schools with unbalanced knowledge in this area. We often encounter a phenomenon that they do not understand the notion of a function, and cannot sketch the graphs of the most common functions, and we do not mention the knowledge of the individual function parameters (e.g. shifts and deformations of the graphs). Without a deeper understanding, students can not apply the knowledge learned in mathematics courses to specialized subjects and practices in general. They cannot even penetrate into more complex mathematical problems, such as solving differential equations.

Based on the initial experience with visualization of graphs of features published in the conference EDULEARN 2018 (Visualisation of parametric functions as a tool for teaching mathematics by Náhlík and Papoušková), we evaluated the usefulness of prepared aids that presented selected graphs of basic functions. We have therefore decided to create a new learning aid, where we discuss trigonometric, exponential and logarithmic functions.

In this article we want to present the parameterized visualizations of trigonometric, exponential and logarithmic functions and multidisciplinary relations into specific fields of study.

Keywords:

Trigonometric function, exponential function, logarithmic function, visualization, graphs, applications.