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 $x$) that the function can accept. 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 number system. 6. So, the domain of $f(x) = \sqrt{x}$ is all real numbers $x$ such that $x \geq 0$, or in interval notation: $[0, \infty)$. 7. The output of $f(x) = \sqrt{x}$ is always $\geq 0$ because square roots are non-negative. 8. Therefore, the range of $f(x) = \sqrt{x}$ is also $[0, \infty)$. 9. To summarize: - Domain: $x \geq 0$ - Range: $y \geq 0$ 10. This means you can only input non-negative numbers into the function, and the outputs will also be non-negative numbers.