Question

Match each of the following asymptotic notation with their correct definition. f(n) and g(n) are some functions ; a and b are constants.

1. Big-θ notation
2. Big-O notation
3. Big-Ω notation
1) Big-θ notation represents the upper bound of a function.
2) Big-O notation represents the lower bound of a function.
3) Big-Ω notation represents the tight bound of a function.
4) Big-θ notation represents the lower bound of a function.
5) Big-O notation represents the tight bound of a function.
6) Big-Ω notation represents the upper bound of a function.

Answer 1

Big-θ notation represents the tight bound of a function. Big-O notation represents the upper bound of a function. Big-Ω notation represents the lower bound of a function.

Step-by-step explanation:

Asymptotic notation is used in computer science to describe the performance characteristics of algorithms and functions. In this context, the correct definitions for the different notations are as follows:

1. Big-θ notation represents the tight bound of a function. It provides both an upper and lower bound, indicating that the function grows at the same rate as the upper and lower bounds.
2. Big-O notation represents the upper bound of a function. It specifies that the function will not grow faster than a certain rate.
3. Big-Ω notation represents the lower bound of a function. It indicates that the function will not grow slower than a certain rate.