1. **State the problem:** We are given the rational function $f(x) = \frac{5}{x - 4}$ and need to analyze its domain, vertical and horizontal asymptotes. 2. **Domain:** The function is undefined where the denominator is zero. Set $x - 4 = 0$ which gives $x = 4$. So, the domain is all real numbers except $x = 4$. 3. **Vertical asymptote:** Vertical asymptotes occur where the denominator is zero and the numerator is nonzero. Here, at $x = 4$, the denominator is zero and numerator is 5, so there is a vertical asymptote at $x = 4$. 4. **Horizontal asymptote:** For rational functions where the degree of numerator is less than the degree of denominator, the horizontal asymptote is $y = 0$. Here, numerator degree is 0 and denominator degree is 1, so horizontal asymptote is $y = 0$. 5. **Summary:** - Domain: all real numbers except $x = 4$ - Vertical asymptote: $x = 4$ - Horizontal asymptote: $y = 0$ 6. **Graph shape:** The graph approaches the vertical line $x=4$ but never touches it, and as $x$ goes to $\pm \infty$, $f(x)$ approaches 0. **Final answer:** - Domain: $x \neq 4$ - Vertical asymptote: $x = 4$ - Horizontal asymptote: $y = 0$