Question

The rule of a function changed from f(x)=x^2-4 to g(x)=(x-3)^2-4 when it was translated.
Can you explain what the translation is from f(x) to g(x)?

Answer 1

if g(x) is f(x-h) then the graph is shifted to the right by h.
So this g(x) is f(x) shifted right by 3.

See
https://www.wolframalpha.com/input/?i=plot+y%3Dx%5E2-4%2C+y%3D%28x-3%29%5E2-4

Answer 2

Thank you!