It looks like you're asking for the long-run behavior of a function as \( x \to \infty \), but I need more information. Could you provide the specific function you're working with? For example, are you asking about a polynomial, rational, exponential, or trigonometric function? 

Once I have the function, I can help analyze its long-run behavior, also known as the limit or asymptotic behavior as \( x \) approaches infinity (or negative infinity).

Let me know!

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Here are 5 follow-up questions related to long-run behavior:
1. Are you working with a specific function or just a general type of function?
2. Do you want to find horizontal asymptotes or the behavior as \( x \to \infty \)?
3. Are there any terms involving \( e^x \), \( \ln(x) \), or trigonometric functions in your problem?
4. Is this part of a calculus problem involving limits or derivatives?
5. Would you like to analyze behavior as \( x \to -\infty \) as well?

**Tip**: For rational functions, the degree of the numerator and denominator often determines the long-run behavior!

Explore how to find the long-run behavior of various functions as x approaches infinity. This guide covers limits, asymptotic behavior, and horizontal asymptotes, and is suitable for high school students in Grades 11-12.

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