What is represented by the variable 'y' in the function rule y = f(x)?

In the function rule ( y = f(x) ), the variable ( y ) represents the output of the function. This means that for every input value ( x ), the function ( f ) produces a corresponding output ( y ). Functions are typically defined as a relationship between input and output, where the function takes an input from its domain (in this case, ( x )) and returns an output (here, ( y )) based on the specific rule defined by ( f ).

Understanding this relationship is essential in mathematics, as it forms the basis for interpreting graphs, analyzing the behavior of functions, and solving equations. Thus, when you see ( y = f(x) ), you can conclude that ( y ) quantifies the result of the function applied to the input ( x ).