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 .