To solve this problem, we need to determine which function has a domain where $x \neq 3$ and a range where $y \neq 2$.

Step 1: Domain Analysis

The domain is restricted by the denominator in rational functions. Any value that makes the denominator zero is excluded from the domain. Let's analyze the denominator of each option:

• Option 1: $f(x) = \frac{x-5}{x+3}$
  • The denominator is $x+3$.