1. Let's clarify what "interval" means in a math context. An interval is a range of numbers between two endpoints, often used to describe where a function is defined or where a solution lies. 2. To figure out an interval, you typically start with the problem's conditions or constraints. For example, if solving inequalities, the solution set is often an interval. 3. If the problem involves a function, the interval might be where the function is increasing, decreasing, or defined. You find this by analyzing the function's domain or critical points. 4. For example, to find where a function $f(x)$ is increasing, you find where its derivative $f'(x) > 0$. The set of $x$ values satisfying this inequality forms an interval or union of intervals. 5. Similarly, to find the domain of a function like $f(x) = \sqrt{x-2}$, you solve $x-2 \geq 0$, giving the interval $[2, \infty)$. 6. In summary, figuring out an interval involves understanding the problem's conditions, solving inequalities or equations, and expressing the solution as a range of values. If you have a specific problem or function in mind, please share it, and I can show you exactly how to find the interval step-by-step.