How the standard function families behave as their input grows large: a logarithm log n increases without bound but ever more slowly, a linear function n increases at a fixed rate, n log n increases slightly faster than linear, and a quadratic n^2 increases in proportion to the square of the input so that doubling n quadruples the value. The mechanism is the shape of each function's output as n is repeatedly scaled up, which yields a strict ordering log n < n < n log n < n^2 for all sufficiently large n. This ordering is what makes one function family meaningfully 'faster-growing' than another.
Big O notation is a formalism from algorithm analysis (computer science, complexity theory) used to describe how the resource cost of an algorithm — measured in number of elementary steps rather than…