Subjects algebra

Function Properties 2A41Ea

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1. **Problem Statement:** Given a graph with two decreasing diagonal lines separated by a vertical dashed red line at $x=1$, answer questions about domain, range, intercepts, and asymptotes. 2. **Domain:** The vertical dashed line at $x=1$ indicates a vertical asymptote, so the function is not defined at $x=1$. Therefore, the domain is all real numbers except $x=1$. In interval notation, this is: $$(-\infty,1) \cup (1,\infty)$$ 3. **Range:** The two diagonal lines extend infinitely downward and upward without horizontal bounds, so the range covers all real numbers. Hence, the range is: $$(-\infty,\infty)$$ 4. **X-intercepts:** From the graph, the function crosses the x-axis at $x=\frac{1}{2}$. So, the x-intercept is: $$x=\frac{1}{2}$$ 5. **Y-intercepts:** The graph crosses the y-axis at $y=2$. So, the y-intercept is: $$y=2$$ 6. **Horizontal Asymptotes:** The graph shows no horizontal asymptotes as the lines continue diagonally without leveling off. Therefore, there are no horizontal asymptotes. 7. **Vertical Asymptotes:** The red dashed vertical line at $x=1$ is a vertical asymptote. So, the vertical asymptote is: $$x=1$$