Input -> Machine -> Output.
Understanding f(x) notation.
Euler introduced the f(x) notation in the 1700s.
The Vertical Line Test tells you if a graph is a function.
Plain English: A function is a machine. You drop a number in (Input/x), it does stuff to it, and spits a number out (Output/y). A valid function never gives two different answers for the same input.
Real-world example: Vending machine. Button A1 always gives Chips. If A1 gave Chips sometimes and Candy other times, it's broken (not a function).
Thinking f(x) means 'f times x'. It doesn't! It's just a name tag.