Challenge:
choose a linear function for f(x) and the same linear function for g(x); then dilate and then translate f(x) and translate and then dilate g(x).
Are the two resulting functions the same? If yes, why? If not, under what circumstances could they be the same?
Challenge:
Choose two different linear functions for f(x) and g(x). Can you use these transformations to transform one into the other? Do you believe you can do the same for any linear f(x) and linear g(x)?
Choose two different quadratic functions for f(x) and g(x). Can you use these transformations to transform one into the other? Do you believe you can do the same for any quadratic f(x) and quadratic g(x)?
Can you transform any quadratic function into a linear function? Why or why not? Prove it.
Challenge:
What additional transformation(s), if any, would you need to be able to transform any cubic function into any other cubic function?