Transformed Functions

Here you can explore how a function changes when its input and output are transformed. You can transform a function both geometrically and algebraically and compare the results. Try to get the algebra to match the geometry.
The function is the base function that will be transformed. To transform it geometrically, use the sliders. To transform it algebraically, use the input boxes. The "pre-transformation" is applied to before it is fed into , the "post-transformation" is applied to the output of (though both use as the place-holder variable). The constants , , , and can be used in these formulae and their values adjusted using the corresponding input boxes. Try seeing what does to for both pre-transformation and post-transformation.