I need help with a question about math.

Question

What is the difference between the function transformations f(x−2)and f(x)+2? Are there any possible functions where these two could result in the same change to the parent function?

Answer 1

Question: What is the difference between the function transformations  and ? Are there any possible functions where these two could result in the same change to the parent function?

Answer: f(x-2) is a function where you take each x, subtract 2, and then plug those numbers in to the function. This is why f(x-2) is a rightward shift of the original f(x) by 2 units. The function f(x) + 2 takes all your x-values in as normal, and then adds 2 to them. This is why f(x) + 2 is an upward shift of the original f(x) by 2 units. So you'll notice that both of these transformations were shifts/translations, and not compression/stretching/etc. I'll leave you to think about functions that result in the same change at the hand of both transformations, but I want you to have some fun with it. Go to a graphing site like Desmos and play around with functions, and see if you find some interesting things!