# 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).