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.