Final answer:
The question involves describing the end behavior of a function as x approaches infinity or negative infinity using proper mathematical notation. This relates to the concept of limits and asymptotes in functions.
Step-by-step explanation:
The student is asking about the end behavior of a function, which is a concept in mathematics that describes what happens to the function's value as x approaches infinity or negative infinity. The correct notation to use would be written as follows:
- As x approaches infinity (x → ∞), f(x) approaches some value L: f(x) → L
- As x approaches negative infinity (x → -∞), f(x) approaches some value M: f(x) → M
If f(x) shows that it is approaching a specific value without ever touching it, this could indicate the presence of a horizontal asymptote, which is a line that a graph gets closer and closer to, but never actually touches or crosses. For example, the function f(x) = 1/x demonstrates end behavior that includes. As x → 0+, f(x) → ∞, representing a vertical asymptote at x = 0. Conversely, as x → ∞, f(x) → 0, indicating a horizontal asymptote at y = 0.