This subject covers the essential concepts and applications of functions in high school mathematics, preparing students for advanced mathematical reasoning.
A function is a special relationship between two sets, where each input has exactly one output. Think of it as a machine: you put something in, and you get something out, but the machine always gives the same result for the same input.
Functions can be expressed in many ways, such as with equations, tables, graphs, or words. The key idea is that every input (usually called \( x \)) is paired with exactly one output (usually called \( y \)). If two different outputs come out for the same input, it's not a function!
Imagine a soda machine: you select a button (input), and you always get the same drink (output). If sometimes you get soda and sometimes juice for the same button, the machine isn't working as a function!
If \( f(x) = x^2 \), then for input 3, output is 9.
A table where each student ID is matched to a grade.
A function pairs each input with exactly one output.