k) \( f(x)=\sqrt{\frac{x-2}{x+3}} \)

This function, \( f(x)=\sqrt{\frac{x-2}{x+3}} \), has some interesting characteristics. First, we need to determine the domain. The expression under the square root must be non-negative, meaning \( \frac{x-2}{x+3} \geq 0 \). This condition holds true when both the numerator and denominator are either both positive or both negative. Solving for these inequalities reveals important values that shape the function's graph. One real-world application of this function could be in modeling scenarios where you're dealing with square roots, such as calculating distances or populations over time constrained by certain limits. For instance, suppose you're analyzing a situation involving the trajectory of a projectile where the height aspects reflect the relationship of functions like this one. Understanding where the function is defined allows you to make meaningful conclusions in physical applications!