Understanding Functions in Mathematics

In Mathematics (the most common specific meaning) Definition: A relationship where every input (from

the domain) has one and only one output (in the range).Notation: Often written as \(y=f(x)\),

read as "f of x," where \(x\) is the input (independent variable) and \(y\) is the output (dependent

variable).Example: \(f(x)=3x\). If you input 2, the output is always 6; if you input

5, the output is always 15.Key Rule: You can't have one input giving multiple

outputs (e.g., \(y^{2}=x\) is a relation, but not a function, because \(x=4\)

gives \(y=2\) and \(y=-2\)).