Final answer:
The function for which it is true that y approaches negative infinity as x approaches infinity is y = 1/x.
Step-by-step explanation:
The function for which it is true that y approaches negative infinity as x approaches infinity is a function of the form y = 1/x.
To understand why this is the case, let's examine the graph of the function y = 1/x. As x approaches infinity (positive values becoming larger), the value of 1/x becomes closer and closer to 0 but never reaches 0. At the same time, as x approaches negative infinity (negative values becoming larger in magnitude), the value of 1/x also becomes closer and closer to 0, but never reaches 0. Therefore, as x approaches infinity, the value of y (1/x) approaches negative infinity.