1. **State the problem:** We analyze the function's domain, range, intercepts, and asymptotes based on the description of a hyperbola-like rational function with two branches. 2. **Domain:** The vertical asymptote is at $x=1$, so the function is undefined there. Thus, the domain is all real numbers except $x=1$. In interval notation: $$(-\infty, 1) \cup (1, \infty)$$ 3. **Range:** The horizontal asymptote is $y=2$, and the branches approach this line but do not cross it. The function has values both above and below $y=2$. Since one branch is in the first quadrant (positive $y$) and the other in the third/fourth quadrants (negative $y$), the range is all real numbers except $y=2$. In interval notation: $$(-\infty, 2) \cup (2, \infty)$$ 4. **x-intercepts:** To find $x$-intercepts, set $y=0$ and solve for $x$. Since the graph crosses the $x$-axis (implied by branches in third/fourth quadrants), there are $x$-intercepts. Exact values depend on the function formula, but since not given, we state: $x=$ values where $y=0$ (exists). 5. **y-intercepts:** Set $x=0$ and find $y$. Since the function is defined at $x=0$ (domain excludes only $x=1$), there is a $y$-intercept. Exact value depends on the function formula. 6. **Horizontal asymptotes:** Given as $y=2$. 7. **Vertical asymptotes:** Given as $x=1$. 8. **Oblique asymptotes:** None, as the function has a horizontal asymptote. **Summary:** - Domain: $$(-\infty, 1) \cup (1, \infty)$$ - Range: $$(-\infty, 2) \cup (2, \infty)$$ - x-intercepts: exist, exact values depend on function - y-intercept: exists, exact value depends on function - Horizontal asymptote: $$y=2$$ - Vertical asymptote: $$x=1$$ - Oblique asymptotes: none Since no explicit function is given, exact intercept values cannot be computed.