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The image contains two rational functions for which you need to determine the domain, range, and asymptotes. Here are the functions:

1. \( y = \frac{2x - 5}{2x + 5} \)
2. \( y = \frac{x^2 - 1}{2x^2 - 3x - 2} \)

Let's break them down one by one.

### 1. \( y = \frac{2x - 5}{2x + 5} \)
- **Domain**: The domain is all real numbers except where the denominator is zero. Solve \( 2x + 5 = 0 \):
  \[
  2x + 5 = 0 \implies x = -\frac{5}{2}
  \]
  So, the domain is \( x \in \mathbb{R} \), \( x \neq -\frac{5}{2} \).

- **Vertical Asymptote**: A vertical asymptote occurs where the denominator is zero. In this case, there is a vertical asymptote at \( x = -\frac{5}{2} \).

- **Horizontal Asymptote**: Compare the degrees of the numerator and the denominator. Since both are linear (degree 1), the horizontal asymptote is determined by the ratio of the leading coefficients:
  \[
  y = \frac{2}{2} = 1
  \]
  Thus, the horizontal asymptote is \( y = 1 \).

- **Range**: The range of the function excludes the horizontal asymptote \( y = 1 \), so the range is \( y \in \mathbb{R}, y \neq 1 \).

---

### 2. \( y = \frac{x^2 - 1}{2x^2 - 3x - 2} \)
- **Domain**: The domain excludes values where the denominator is zero. Factor the denominator:
  \[
  2x^2 - 3x - 2 = (2x + 1)(x - 2)
  \]
  So, the domain is all real numbers except \( x = -\frac{1}{2} \) and \( x = 2 \).

- **Vertical Asymptotes**: Vertical asymptotes occur where the denominator is zero. From the factored form, we get vertical asymptotes at:
  \[
  x = -\frac{1}{2}, \quad x = 2
  \]

- **Horizontal Asymptote**: Since the degrees of the numerator and denominator are the same (degree 2), the horizontal asymptote is determined by the ratio of the leading coefficients:
  \[
  y = \frac{1}{2}
  \]
  So, the horizontal asymptote is \( y = \frac{1}{2} \).

- **Range**: The range excludes the horizontal asymptote \( y = \frac{1}{2} \), so the range is \( y \in \mathbb{R}, y \neq \frac{1}{2} \).

---

Would you like more details or explanations on any of these points?

### Related Questions:
1. How do you determine slant (oblique) asymptotes for rational functions?
2. What is the general method to find the domain of any rational function?
3. Can a rational function have both a horizontal and slant asymptote?
4. What are the conditions for a rational function to have no horizontal asymptote?
5. How do you determine the behavior of a function near its vertical asymptote?

**Tip**: Always check if a rational function can be simplified before analyzing its asymptotes and other characteristics.

Determine the domain, range, and asymptotes for the following rational functions: 1) y = (2x - 5) / (2x + 5), 2) y = (x^2 - 1) / (2x^2 - 3x - 2).

Learn how to find the domain, range, and asymptotes for the rational functions y = (2x - 5) / (2x + 5) and y = (x^2 - 1) / (2x^2 - 3x - 2). This step-by-step solution is ideal for students in Grades 10-12, covering key concepts of rational functions and asymptotes.

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