Przekształcenia wykresów funkcji

Abstract

This article is concerned with some topics of the transformations of the graphs of functions. It is designated to serve as a text for the students of mathematics (prospective teachers) and the teachers of mathematics. In this paper we give the answer to the following problem: Given the graph of the function $f:R ⊇ D_f → R$. Construct the graph of the function $F:R ⊇ D_F → R$ de ned by the rule $F(x) = cf(ax + b) + d$, where $a,c ∈ R $\$ {\{0}\}, b,d ∈ R$ are constant numbers and $D_F = {\{x ∈ R : ax + b ∈ D_f}\}$. Some connections between the oddness, the evenness, and the periodicity of the functions $f$ and $F$ are considered. The arrangement of the theoretical topics is a didactic suggestion for school teaching concerning the transformations of the graphs of functions.