1. **Problem Statement:** Given a rational function $f$ with a vertical asymptote at $x=0$ and a horizontal asymptote at $y=2$, find the equations of the asymptotes, the $x$- and $y$-intercepts, and the domain and range. 2. **Asymptotes:** - Vertical asymptote occurs where the denominator is zero and the function is undefined. - Horizontal asymptote describes the end behavior of the function as $x \to \pm \infty$. 3. **Given:** - Vertical asymptote: $x=0$ - Horizontal asymptote: $y=2$ 4. **Intercepts:** - $x$-intercepts occur where $f(x)=0$. - $y$-intercepts occur where $x=0$. 5. **From the graph:** - No $x$-intercepts are marked, so none exist. - No $y$-intercepts are marked, so none exist. 6. **Domain:** - All real numbers except where the function is undefined. - Since vertical asymptote at $x=0$, domain is $$(-\infty,0) \cup (0,\infty)$$ 7. **Range:** - The function approaches but never reaches $y=2$. - No values at $y=2$, so range is $$(-\infty,2) \cup (2,\infty)$$ **Final answers:** - Vertical asymptote(s): $x=0$ - Horizontal asymptote(s): $y=2$ - $x$-intercept(s): None - $y$-intercept(s): None - Domain: $(-\infty,0) \cup (0,\infty)$ - Range: $(-\infty,2) \cup (2,\infty)$