Question

Explain what it means for a function to be \(O(1)\)

Short answer

A function is meant to be \(O(1)\) when constants exists such that \(\left| {f(x)} \right| \le C\left| 1 \right|\), \(x > k\)

Step-by-step solution

Step 1:

A function \(f\) is \(O(1)\) if \(\left| {f(x)} \right| \le C\) for all sufficiently large \(x\), where \(C\) is constant

Step 2:

In other words, function \(f\) is \(O(1)\) if its absolute value is bounded for all \(x > k\) . Here \(k\) is some constant.