1. Let's start by defining a function. In mathematics, 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. 2. More formally, if $f$ is a function from set $A$ to set $B$, written as $f: A \to B$, then for every $a \in A$ there is a unique $b \in B$ such that $f(a) = b$. 3. Functions can be represented in many forms: formulas (e.g., $f(x) = x^2$), graphs, or tables. 4. Uses of functions in real life include: - Modeling relationships, like how distance changes over time (speed functions). - Economics: profit functions to optimize revenue. - Computer science: functions are blocks of code that perform specific tasks. - Physics: describing motion, force, energy as functions of variables. - Medicine: dosage-response functions to determine treatment levels. 5. Understanding functions helps us analyze and predict real-world phenomena systematically, making complex systems understandable and manageable.