Final answer:
The student's question pertains to the end behavior of functions in mathematics, specifically as x approaches negative infinity. The function's values either approach positive or negative infinity, which is related to the function's asymptotic behavior.
Step-by-step explanation:
The question provided deals with the concept of end behavior of functions in mathematics. End behavior describes the trend of a function as the input variable (x) approaches infinity (either positive or negative). The description provided, 'y → +∞ as x → -∞,' signifies that as the value of x decreases without bound (moves towards negative infinity), the value of the function (y) increases without bound (moves towards positive infinity). Conversely, the phrase 'y → -∞ as x → -∞' suggests that as x approaches negative infinity, the function value decreases without bound (approaching negative infinity).
This behavior is often seen in functions that have asymptotes, which are lines that a graph approaches but never touches. Functions like y = 1/x are classic examples where y approaches infinity as x approaches zero from the positive side. Also, certain other functions, depending on their degree and leading coefficient, will have specific end behaviors that can be predicted using polynomial end behavior patterns.
Considering derivatives and continuous functions, the first derivative of a function signifies the instantaneous rate of change and for a behavior pattern to be predictable, these derivatives also need to be continuous unless there's an infinite discontinuity involved.