https://file.aiquickdraw.com/mathbot/file/172885822420135bn357p.jpg

https://file.aiquickdraw.com/mathbot/file/1728858224202tumqfaes.jpg

The given images contain the following mathematical prompt:

### Function:
Consider the rational function:
\[
f(x) = \frac{2x^2 + 7x + 3}{x^2 - x - 12}
\]
and answer the following questions.

The second image seems to contain some additional questions related to this function, likely about asymptotes or behavior at certain limits.

Would you like me to help break down the rational function or tackle specific questions related to it, such as vertical/horizontal asymptotes, domain, or behavior at infinity?

### Some related questions to consider:
1. How do you find the vertical asymptotes of a rational function?
2. What are the steps to determine horizontal asymptotes of a rational function?
3. How do we determine the domain of this rational function?
4. What happens to \( f(x) \) as \( x \to \infty \) or \( x \to -\infty \)?
5. Can we simplify \( f(x) \) by factoring both the numerator and the denominator?

#### Tip: 
To find vertical asymptotes, focus on where the denominator becomes zero. For horizontal asymptotes, compare the degrees of the numerator and denominator!

Consider the rational function f(x) = (2x^2 + 7x + 3) / (x^2 - x - 12) and answer the following questions.

This lesson explores the rational function f(x) = (2x^2 + 7x + 3) / (x^2 - x - 12). Learn how to determine vertical and horizontal asymptotes, analyze domain, and simplify rational functions. Suitable for students in Grades 10-12.

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