1. The problem is to understand what a function is and how it works. 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 formula for a function is usually written as $f(x)$, where $x$ is the input and $f(x)$ is the output. 4. Important rules: - Each input $x$ must have only 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 doubles the input and adds 3 to get the output. 7. Functions can be graphed, and the graph shows how the output changes with the input. 8. Understanding functions helps in many areas of math and science because they describe relationships between quantities.