The line y = 4 is a horizontal asymptote to the right of the graph of a function f. What is the limit of f as x approaches infinity?

Understanding the Concept of Horizontal Asymptotes

A horizontal asymptote indicates the behavior of a function as the variable approaches infinity. When we say that the line $y = 4$ is a horizontal asymptote to the right of the graph of a function $f$, it implies that as $x$ becomes very large (approaching infinity), the value of the function $f(x)$ approaches the value of the asymptote.

Evaluating the Limit

1. Statement of the Limit Definition: The limit of $f(x)$ as $x$ approaches infinity can be expressed mathematically as: $\lim_{x \to \infty} f(x)$

2. Asymptotic Behavior: Given that the line $y = 4$ is a horizontal asymptote, we know: $\lim_{x \to \infty} f(x) = 4$

Final Answer

Thus, the limit of $f$ as $x$ approaches infinity is:

$\lim_{x \to \infty} f(x) = 4$