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remplis les trous de la phrase par les resultat

To fill in the blanks, let's analyze the requirements step by step.

The question asks us to show that the function \( f \) has an asymptote given by the line \( y = -2 \) as \( x \) approaches \( +\infty \). For a horizontal asymptote \( y = L \) as \( x \to +\infty \), we need to demonstrate that:

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

In this case, \( L = -2 \).

Thus, the complete sentence with the blanks filled in would be:

> la limite de \( f(x) \) quand \( x \) tend vers \( +\infty \) est égale à \( -2 \).

So:
1. First blank: \( +\infty \)
2. Second blank: \( -2 \)

Would you like a more detailed explanation on how limits relate to asymptotes, or do you have any further questions?

Here are 5 related questions to expand on this concept:
1. How do we determine if a function has a vertical asymptote?
2. Can a function have more than one horizontal asymptote?
3. How does the behavior of \( f(x) \) at \( -\infty \) influence the asymptote?
4. What is the difference between horizontal and oblique asymptotes?
5. How do we calculate limits involving infinity in rational functions?

**Tip:** To confirm if a function has a horizontal asymptote at a specific value, calculate its limit as \( x \) approaches infinity.

remplis les trous de la phrase par les résultat

Learn how to find the horizontal asymptote of a function by analyzing the limit as x approaches positive infinity. This example demonstrates that the curve approaches the line y = -2 as an asymptote when the limit of f(x) as x tends to infinity equals -2. Suitable for students in Grades 10-12.

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