1. **Problem Statement:** Given the graph of a rational function $f$ with vertical and horizontal asymptotes and intercepts, find: - (a) Equations of vertical and horizontal asymptotes. - (b) Domain and range of $f$. - (c) All $x$- and $y$-intercepts. 2. **Asymptotes:** - Vertical asymptote occurs where the function is undefined and the graph tends to infinity. - Horizontal asymptote describes the behavior of $f(x)$ as $x \to \pm \infty$. 3. **From the graph description:** - Vertical asymptote at $x=2$. - Horizontal asymptote at $y=0$. 4. **Domain:** - All real numbers except where vertical asymptotes occur. - So, domain is $(-\infty, 2) \cup (2, \infty)$. 5. **Range:** - The graph approaches $y=0$ but never touches it. - On the left side, $f(x)$ is positive and tends to $+\infty$ near $x=2$. - On the right side, $f(x)$ is negative and tends to $-\infty$ near $x=2$. - So, range is $(-\infty, 0) \cup (0, \infty)$. 6. **Intercepts:** - $x$-intercepts are points where $f(x)=0$. - From the graph, no $x$-intercepts are shown. - $y$-intercept is $f(0)$. - The graph is above $y=0$ for $x<2$, so $f(0)>0$. - Given options for $y$-intercept are 1, 2, 6, or None. - The graph likely crosses $y=1$ at $x=0$. **Final answers:** - (a) Vertical asymptote: $x=2$ and Horizontal asymptote: $y=0$ - (b) Domain: $(-\infty, 2) \cup (2, \infty)$ Range: $(-\infty, 0) \cup (0, \infty)$ - (c) $x$-intercept(s): None $y$-intercept(s): 1