There are several types of transformation of functions, being the most common: Reflection (vertical or horizontal) and Translation (vertical or horizontal). In mathematics, the use of these transformations in the plane constitutes a valuable instrument, as an aid to the construction of function graphs. Knowing a set of "fundamental graphs" and applying some knowledge of transformations, we can obtain several other graphs from the originals.
To learn more about this subject, see this page of Transformations of the Graph of a Function, which contains a summary of all the transformations you need to know.
Created with GeoGebra by Vitor Nunes
Choose one of several types of transformations and then move the "selector" that controls the value of variable `a`. Notice the differences between the chosen function and the original green color function.
Function is one of the most important concepts in mathematics. Although there are several definitions of function, they are usually defined by the existence of a certain relation between two sets. Because of their generality, functions appear in many mathematical contexts, and many areas of mathematics are based on the study of functions. The concept of Function is a generalization of the common notion of mathematical formula. Functions describe special mathematical relationships between two sets. Intuitively, a function is a way of associating each value of an element `x` (called an independent variable) with a single value of `y`, resulting in `f(x)` (called a dependent variable). This can be done through an equation, a graphical relationship, a diagram representing two sets, an association rule (called algebraic expression), or through a matching table. Each pair of elements related by the function determines a point `P(x, y)`.