Functions and Function Machines
Think of functions as mathematical machines that take a number, do something to it, and spit out a result. They're brilliant for describing how one value changes based on another.
Function machines show this process visually. You put a number in one end, it goes through operations like+7then×3, and you get your answer out the other side. It's like following a step-by-step recipe!
Function notation uses letters like f, g, or h to name your function. When you see f(x) = 5x - 3, the "f" is your function's name, and it's telling you to multiply x by 5, then subtract 3. Much tidier than writing it out every time!
Quick Tip: Function notation is just a fancy way of writing "do this to x" - don't let the symbols intimidate you!
Functions become really powerful when you learn about inverse functions (which undo what the original function did) and composite functions (which combine multiple functions). If f(x) = x + 5, then f⁻¹(x) = x - 5 reverses it perfectly.