https://file.aiquickdraw.com/mathbot/file/1730824448877teajstl2.jpg

The function provided in the image is:

\[
y = \frac{x^2 + 3x}{x - 1}
\]

If you would like to analyze this function, there are several directions we could explore. For example, we could find:

1. The domain and range of the function.
2. Any asymptotes, both vertical and horizontal.
3. The derivative \( y' \) for finding slopes and critical points.
4. The behavior of \( y \) as \( x \to \infty \) or \( x \to -\infty \).
5. Points of discontinuity or special behavior.

Would you like to explore one of these aspects or have a specific question about this function?

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### Relative Questions
1. How do we find the domain of a rational function?
2. What are the steps to determine vertical and horizontal asymptotes?
3. How can we apply differentiation to find critical points in this function?
4. How does the behavior of the function change near points of discontinuity?
5. What are possible applications of this type of function in real-life scenarios?

**Tip:** For rational functions, always start by identifying points where the denominator is zero to understand discontinuities and asymptotes.

Explore the characteristics of the rational function y = (x^2 + 3x) / (x - 1). This analysis includes determining the domain, asymptotes, derivative, and behavior near points of discontinuity. Suitable for high school students in Grades 10-12.

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