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High School Mathematics - 2
Identity, Constant and Equal Functions

Constant Function
A function f: A ->B is called a constant function if every element of A is associated with the same element of B, i.e the range of f consists of only one element as shown.

Example: Let A = {2,3,5,7,11} and B = {0,7,14, 21}, then f = {(2,0), (3,0), (5,0),(7,0), (11,0)} is a constant function.

Identity Function
Let A be any set. A function f: A ->A is called an identity function if for every x A,f(x) = x. i.e if every element is mapped onto itself. It is denoted as IA. Then IA(x) = x for all x A.

Example: Let A = {1,2,3,4}, then f = {(1,1), (2,2), (3,3), (4,4) } is an identity function.

Equal Function
Two functions f and g are said to be equal written as f = g if they have the same domain and they satisfy the condition f(x) = g(x) for all x.
Example: Consider function f defined as shown below in the diagram

let a function g be defined by the formula g(x) = x2 where the domain of g is {1,2}. Then f = g since they both have the same domain and since f and g both assign the same image to each element in the domain.

Directions: Answer the following.