3) \( f(x)=\frac{e^{-3 x}}{3 x-5} \)

The function \( f(x) = \frac{e^{-3x}}{3x - 5} \) combines an exponential decay in the numerator with a linear expression in the denominator. As \( x \) approaches \( \frac{5}{3} \), the function becomes undefined due to division by zero, creating a vertical asymptote. This means that while the exponential term tends to zero as \( x \) increases, the denominator's linear growth can lead to interesting behaviors near that critical point. In real-world scenarios, functions similar to this can model various phenomena, such as population decay in the face of resource constraints or the diminishing returns in production processes. Understanding how one component influences the other—like exponential decay versus linear growth—can yield insights into optimizing systems or predicting behaviors over time.