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The given function is:

\[
f(x) = \frac{x - 3}{x + 5}
\]

Let's go through the steps to solve the problem:

### 1. **Domain:**
The domain consists of all real numbers except where the denominator equals zero (since division by zero is undefined).

Set the denominator equal to zero and solve:
\[
x + 5 = 0 \implies x = -5
\]

So, the domain is:
\[
(-\infty, -5) \cup (-5, \infty)
\]

### 2. **X-intercept:**
The x-intercept occurs when \( f(x) = 0 \), which means the numerator of the function equals zero.

Set \( x - 3 = 0 \) and solve:
\[
x = 3
\]

Thus, the x-intercept is at \( (3, 0) \).

### 3. **Y-intercept:**
The y-intercept occurs when \( x = 0 \).

Substitute \( x = 0 \) into the function:
\[
f(0) = \frac{0 - 3}{0 + 5} = \frac{-3}{5}
\]

Thus, the y-intercept is at \( \left(0, -\frac{3}{5}\right) \).

### 4. **Asymptotes:**

- **Vertical Asymptote:**
  The vertical asymptote occurs where the denominator equals zero, which we've already found to be at \( x = -5 \).
  
- **Horizontal Asymptote:**


List the domain and the x- and y-intercepts of the function f(x) = (x - 3) / (x + 5). Graph the function. Be sure to label all the asymptotes.

Explore the rational function f(x) = (x - 3) / (x + 5). Learn how to determine the domain, find the x- and y-intercepts, and identify vertical and horizontal asymptotes. Includes step-by-step calculations and graphing tips. Suitable for high school students studying algebra or pre-calculus.

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