1. Let's start by understanding what domain and range mean in math. 2. The **domain** of a function is the set of all possible input values (usually $x$) for which the function is defined. 3. The **range** of a function is the set of all possible output values (usually $y$) that the function can produce. 4. For example, consider the function $f(x) = \sqrt{x}$. 5. The square root function is only defined for $x \geq 0$ because you cannot take the square root of a negative number in the real numbers. 6. So, the domain of $f(x) = \sqrt{x}$ is $\{x \mid x \geq 0\}$. 7. The output of $f(x)$ is always $\geq 0$ because square roots are non-negative. 8. Therefore, the range of $f(x) = \sqrt{x}$ is $\{y \mid y \geq 0\}$. 9. To summarize: - Domain: all $x$ values where the function works. - Range: all $y$ values the function outputs. 10. This helps us understand where a function is valid and what values it can produce.