Transformations of Functions and Graphs

Topic:
Functions
Given a function and its graph, by applying certain transformations to the graph, we can obtain the graphs of certain related functions. There are three types of transformations: translations, scalings and reflections. A. Translations Translating the graph towards the right/left by unit(s): It is the graph of , when is positive/negative. Translating the graph upwards/downwards by unit(s): It is the graph of , when is positive/negative. B. Scalings Stretching/compressing the graph along the y-axis by a factor of / : It is the graph of , when is greater/smaller than 1. Compressing/stretching the graph along the x-axis by a factor of / : It is the graph of , when is greater/smaller than 1. C. Reflections Reflection across y-axis: It is the graph of . Reflection across x-axis: It is the graph of .