1. **State the problem:** We are given the function $f(x) = \frac{1}{x - 3} - 1$ and need to analyze its properties. 2. **Identify key features:** This is a rational function with a vertical asymptote where the denominator is zero and a horizontal asymptote based on the behavior as $x \to \pm \infty$. 3. **Vertical asymptote:** Set denominator equal to zero: $$x - 3 = 0 \implies x = 3$$ So, there is a vertical asymptote at $x = 3$. 4. **Horizontal asymptote:** As $x \to \pm \infty$, the term $\frac{1}{x-3} \to 0$, so $$f(x) \to 0 - 1 = -1$$ Thus, the horizontal asymptote is $y = -1$. 5. **Summary:** The function has a vertical asymptote at $x=3$ and a horizontal asymptote at $y=-1$. 6. **Graph features:** The function is undefined at $x=3$, and the graph approaches $y=-1$ as $x$ becomes very large or very small. Final answer: The function $f(x) = \frac{1}{x - 3} - 1$ has vertical asymptote $x=3$ and horizontal asymptote $y=-1$.