https://file.aiquickdraw.com/mathbot/file/1725603498860da4a9cwj.jpg

The image contains a mathematical problem involving a function and its behavior as the input approaches infinity. Let's extract and analyze the problem and then provide a solution.

### Problem Analysis
The problem seems to ask about the limit of a given function \( f(x) \) as \( x \) approaches infinity. From the graph:
- The function appears to approach a horizontal asymptote, specifically the line \( y = 0 \) as \( x \) increases.
- The task is to determine the value of this limit.

### Solution
From the graph, it is evident that as \( x \to \infty \), the function \( f(x) \) gets closer and closer to the x-axis, suggesting that the function approaches zero. Thus, the limit of the function as \( x \to \infty \) is:

\[
\lim_{x \to \infty} f(x) = 0
\]

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### Related Questions:
1. What does a horizontal asymptote indicate about a function's behavior?
2. How can you formally prove a limit using algebraic techniques?
3. What are some common functions with horizontal asymptotes?
4. How does the concept of limits apply to real-world scenarios?
5. What is the importance of understanding function behavior at infinity?

### Tip:
Always look for asymptotes in a graph, as they provide valuable information about the function's behavior as it approaches extreme values.

What is the limit of the function as x approaches infinity, based on the graph provided?

Understand how to determine the limit of a function as x approaches infinity using a graph. This problem highlights key concepts of limits and asymptotes, providing insight into the function's behavior as it tends towards a horizontal asymptote.

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