function and graphs

Functions

• A function is a relationship or rule that connects each input to exactly one output. In other words, for every element in the domain (input), there is one corresponding element in the range (output). 

• Notation: We often write functions as f(x),where f is the name of the function and x is the input. 

• Example: f(x) = 2x + 1. Here, if we input x = 3, the function outputs 2(3) + 1 = 7.

Domain: The set of all possible inputs for which the function is defined. 

Range: The set of all possible outputs of the function.