Does a function $f$ exists such that: $f(n-k) \ne \Theta(f(n))$ for some constant $k\geq1$?

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 $ k\geq1$ ?"

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