**Big-Theta** is the tight bound or average bound of a function is denoted as *notation* (**Θ**).

**Definition:** Suppose we have two functions **f(n)** and **g(n)**, then the function **f(n) = Θ(g(n)** if and only if there exists three positive constants **c1**, **c2**, and **k**, such that **c1 * g(n) <= f(n) <= c2 * g(n)** for all **n >= k**.

For example:

Suppose, if **f(n) = 2 * n + 3**, then

**1 * n <= 2 * n + 3 <= 5 * n** for all n >= 1.

In the above equation,

c1 = 1, c2 = 5, k = 1, and g(n) = n

Now we know that, 1< log(n) < n^(1/2) < **n** < n log(n) < n^2 < n^3 < — < 2^n < 3^n <---- n^n.

In the above comparison, n is the tight bound.

This symbolizes,

- f(n) = Θ(n) —
**True** - f(n) = Θ(n^2) —
**False** - f(n) = Θ(1) —
**False**, and so on…

**That is, in Big-Theta, we have only one g(n), which in this case is **Θ(n)**.