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When we talk about functions in math, especially numerical functions, we're talking about a relationship between two sets of numbers. You have an input number (often called 'x') and an output number (often called 'y' or 'f(x)').

In math, functions describe how one quantity changes in relation to another. For example, how much you earn ($y$) might depend on how many hours you work ($x$). Linear and affine functions are the simplest, yet most powerful, ways to describe these relationships when they form a straight line.

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When you look at a function's graph, you're essentially mapping inputs (on the x-axis) to outputs (on the y-axis) and vice versa.

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When we talk about the variation of a function, we're simply describing how its output (y-value) changes as its input (x-value) increases.

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When you operate on functions, you're essentially performing arithmetic or composition with their output values.

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