Trig Functions and Plane Transformations

This example is based on the function . If you want to explore another function, type its new expression in the input field, then confirm pressing the Enter key. How does the function graph modify if we apply some "classic" transformations (horizontal and vertical translations, dilations, composition with function, etc) ? Before viewing the resulting graph, try to determine the new position of some "convenient" points related to the function (e.g. the intersections with the coordinate axes), as well as the possible variations of the main characteristics of the function (amplitude, period...). Move the slider α to view dynamically the magnitudes of translations and dilations.