Investigating Succesive transformations
Investigate the effect of successive transformations on a function. Use the input box to enter a function. Use one of the four options at the bottom of the right-hand screen and the sliders to select a new function based on the original (use a = -1 for a reflection). Now consider the two possible sequences of transformations that you could apply to reach the new function; use the check boxes to reveal the graphs of the successive transformations; do they both work?
Consider the order that transformations in a sequence are carried out: When is the order important, when is it not? In which cases do you need to translate then stretch and when should you stretch and then translate? Test out your ideas on some different functions.