1. **State the problem:** Find the function $f(x)$ given by the expression. 2. **Given:** $$f(x) = \frac{8}{x^2 - 2x - 3}$$ 3. **Factor the denominator:** $$x^2 - 2x - 3 = (x - 3)(x + 1)$$ 4. **Rewrite the function:** $$f(x) = \frac{8}{(x - 3)(x + 1)}$$ 5. **Interpretation:** This is a rational function with vertical asymptotes where the denominator is zero, i.e., at $x=3$ and $x=-1$. 6. **Final answer:** $$f(x) = \frac{8}{(x - 3)(x + 1)}$$