Final answer:
The function where y approaches negative infinity as x approaches positive infinity is an inverse proportionality function such as y = -1/x, which exhibits a hyperbolic decay.
Step-by-step explanation:
The question asks for the function where y → -∞ (y approaches negative infinity) as x → ∞ (x approaches positive infinity). The function that exhibits this behavior is a function with a horizontal asymptote as x becomes very large (positively). A classic example of a function where y approaches negative infinity as x approaches positive infinity is y = -1/x. As x gets larger, y becomes more negative, tending towards negative infinity. This is an example of an inverse proportionality relationship where y is inversely proportional to x, and it presents a hyperbolic decay as it approaches its horizontal asymptote.