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: