b) \( y=\frac{x}{1-x^{2}} \)

This function has an interesting behavior! The denominator \(1 - x^2\) reveals critical points, specifically at \(x = 1\) and \(x = -1\), where the function becomes undefined, leading to vertical asymptotes. As \(x\) approaches these values, \(y\) will trend towards positive or negative infinity. This is a classic example of a rational function illustrating how asymptotes can shape the graph's behavior dramatically near their points of discontinuity. In real-world applications, such functions can model scenarios where resources become limited, like population growth constrained by carrying capacity or the effectiveness of a drug as it approaches saturation. In these cases, knowing where discontinuities occur can help in making predictions and managing expectations, akin to navigating around obstacles in life's road map!