asymptotics – Does a function $f$ exists such that: $f(n-k) ne Theta(f(n))$ for some constant $kgeq1$?


I have encountered the following question in my homework assignment in Data Structures course:

“Does a function $f$ exists such that: $f(n-k) ne Theta(f(n))$ for some constant $kgeq1$ ?”

I think no such function $f$ exists, but I do not know how to prove it (or give a counter-example if one exists).