1. The problem asks us to find the domain of the rational function $$f(x) = \frac{5}{x - 6}$$ and understand its graph. 2. The domain of a rational function includes all real numbers except where the denominator equals zero because division by zero is undefined. 3. Set the denominator equal to zero to find excluded values: $$x - 6 = 0$$ 4. Solve for $$x$$: $$x = 6$$ 5. Therefore, the domain is all real numbers except $$x = 6$$. In interval notation, the domain is: $$(-\infty, 6) \cup (6, +\infty)$$ 6. The graph has a vertical asymptote at $$x = 6$$ where the function is undefined. 7. The graph approaches zero (the x-axis) horizontally as x approaches $$\pm \infty$$, so there is a horizontal asymptote at $$y = 0$$. 8. Summary: - Domain: all real numbers except $$6$$. - Vertical asymptote: $$x=6$$. - Horizontal asymptote: $$y=0$$. Final Answer: $$\text{Domain} = \{ x \in \mathbb{R} : x \neq 6 \}$$