1. The problem is to understand the concept of a function in mathematics. 2. A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output. 3. The notation for a function is usually $f(x)$, where $x$ is the input and $f(x)$ is the output. 4. Important rules: - Each input $x$ must have exactly one output $f(x)$. - Different inputs can have the same output. 5. For example, if $f(x) = 2x + 3$, then for $x=1$, $f(1) = 2(1) + 3 = 5$. 6. This means the function takes the input 1 and maps it to the output 5. 7. Functions can be represented by formulas, tables, graphs, or words. 8. Understanding functions is fundamental in algebra and many areas of mathematics.