1. **Problem Statement:** We analyze a hyperbola-like rational function with two branches, having vertical asymptote at $x=1$ and horizontal asymptote at $y=2$. 2. **Domain:** The vertical asymptote at $x=1$ means the function is undefined at $x=1$. Thus, the domain is all real numbers except $x=1$. In interval notation: $$(-\infty, 1) \cup (1, \infty)$$ 3. **Range:** The horizontal asymptote at $y=2$ means the function approaches but never equals $y=2$. Since the branches extend infinitely above and below, the range is all real numbers except $y=2$. In interval notation: $$(-\infty, 2) \cup (2, \infty)$$ 4. **X-intercepts:** X-intercepts occur where $y=0$. Given the graph's description, there are no x-intercepts. 5. **Y-intercepts:** Y-intercepts occur where $x=0$. Given the graph's description, there are no y-intercepts. 6. **Horizontal Asymptotes:** The horizontal asymptote is $y=2$. 7. **Vertical Asymptotes:** The vertical asymptote is $x=1$. 8. **Oblique Asymptotes:** There are no oblique asymptotes. **Final answers:** - Domain: $$(-\infty, 1) \cup (1, \infty)$$ - Range: $$(-\infty, 2) \cup (2, \infty)$$ - X-intercepts: None - Y-intercepts: None - Horizontal asymptote: $$y=2$$ - Vertical asymptote: $$x=1$$ - Oblique asymptotes: None