Determine the vertical and horizontal asymptote of the function f(x)=(5x-3)/(2x+3) and plot in the confession coordinate 

The graph of the function \( f(x) = \frac{5x - 3}{2x + 3} \) has been plotted. It shows:

- A **vertical asymptote** at \( x = -\frac{3}{2} \) (red dashed line).
- A **horizontal asymptote** at \( y = \frac{5}{2} \) (green dashed line).

Would you like further details or have any questions about the asymptotes or the plot?

Here are some related questions for further exploration:
1. What happens to \( f(x) \) as \( x \to \infty \) and \( x \to -\infty \)?
2. How would adding constants to the numerator or denominator affect the asymptotes?
3. Can \( f(x) \) intersect its horizontal asymptote?
4. What would the graph look like if the denominator's degree was higher than the numerator's?
5. How do the horizontal and vertical asymptotes affect the general shape of rational functions?

**Tip**: Always check the domain of a rational function by setting the denominator equal to zero to avoid undefined points.

Determine the vertical and horizontal asymptote of the function f(x)=(5x-3)/(2x+3) and plot in the confession coordinate.

Learn how to determine the vertical and horizontal asymptotes of the rational function f(x) = (5x-3)/(2x+3). This problem covers key concepts in algebra, including finding asymptotes and graphing rational functions. Suitable for students in Grades 10-12.

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