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Here's the graph of the function \( k(x) = \frac{3x - 15}{x + 2} \), including:

1. **Vertical Asymptote** at \( x = -2 \) (red dashed line).
2. **Horizontal Asymptote** at \( y = 3 \) (green dashed line).
3. **Key Points** labeled near the vertical asymptote to provide insight on the behavior of \( k(x) \) around \( x = -2 \).

This graph helps visualize how the function approaches these asymptotes. Would you like more details on any specific aspect, or have further questions?

Here are some related questions you might find useful:
1. How can we determine the slant asymptote for rational functions?
2. What are the steps for finding horizontal asymptotes for different types of functions?
3. How would this graph change if we modified the function to \( \frac{3x - 15}{x - 2} \)?
4. Can we determine the domain and range of this function from the graph?
5. What are some common methods for factoring rational functions?

**Tip:** When graphing rational functions, always check both the numerator and denominator for common factors; canceling these can reveal holes instead of vertical asymptotes.

Graph the function \( k(x) = \frac{3x - 15}{x + 2} \) including all necessary asymptotes. For vertical asymptotes, ensure there are at least two points on each side.

Learn how to graph the rational function k(x) = (3x - 15) / (x + 2), focusing on identifying vertical and horizontal asymptotes. Includes a step-by-step approach to plot necessary points and asymptotes for a complete graph. Suitable for high school students in Grades 11-12.

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