What do you mean by the utility function?

The Utility Function:

Sometimes this is easier to work directly along with the preference relation and its connected sets. Although other times, particularly when one wants to use calculus processes, this is easier to work along with preferences which can be represented by a utility function; which is, a function u: X → R that is:

xy if and only if u(x) ≥ u(y). Some examples of utility functions are as follows:

a. Cobb-Douglas Utility Function)

b. Linear Utility Function

c. Leontief Utility Function

d. Existence of a Utility Function

e. Non-Representation of Lexicographic Ordering by a Function

f. Invariance of Utility Function to Monotonic Transforms