1. **Problem:** Use the graph to answer questions about values of $x$ and $y$. (a) For what values of $x$ is $y=1$? - From the graph, $y=1$ approximately at $x \approx -2.5$ and $x \approx 2.5$. (b) For what values of $x$ is $y=3$? - The graph does not reach $y=3$, so no $x$ values satisfy $y=3$. (c) For what values of $y$ is $x=3$? - At $x=3$, $y$ is approximately $0$. (d) For what values of $y$ is $x \leq 0$? - For $x \leq 0$, $y$ ranges from about $-1$ to $2$. (e) What are the maximum and minimum values of $y$ and for what $x$? - Maximum $y \approx 2$ at $x \approx -1$. - Minimum $y \approx -2$ at $x \approx 1$. 2. **Problem:** Use the table to answer Exercise 1 questions. (a) $y=1$? - No $y=1$ in table. (b) $y=3$? - No $y=3$ in table. (c) $x=3$? - $y=-1$ at $x=3$. (d) $x \leq 0$? - $x=-2,-1,0$ with $y=5,-1,-2$ respectively. (e) Max and min $y$? - Max $y=9$ at $x=5$. - Min $y=-2$ at $x=0$. 3. **Problem:** Determine if graphs define $y$ as a function of $x$. (a) Passes vertical line test, so yes. (b) Passes vertical line test, so yes. (c) Fails vertical line test, so no. (d) Circle fails vertical line test, so no. 4. **Problem:** Compare natural domains of $f$ and $g$. (a) $f(x) = \frac{x^2 + x}{x+1} = \frac{x(x+1)}{x+1}$, undefined at $x=-1$. - Domain of $f$: all real $x \neq -1$. - Domain of $g(x) = x$: all real numbers. (b) $f(x) = \frac{x\sqrt{x} + \sqrt{x}}{x+1} = \frac{\sqrt{x}(x+1)}{x+1}$, undefined at $x=-1$ and requires $x \geq 0$ for $\sqrt{x}$. - Domain of $f$: $x \geq 0$, $x \neq -1$ (but $-1$ excluded anyway since $x \geq 0$). - Domain of $g(x) = \sqrt{x}$: $x \geq 0$. Hence, domain of $f$ is $[0, \infty)$ and domain of $g$ is $[0, \infty)$. Final answers summarized: - Exercise 1: (a) $x \approx -2.5, 2.5$; (b) no $x$; (c) $y \approx 0$; (d) $y \in [-1,2]$; (e) max $y=2$ at $x=-1$, min $y=-2$ at $x=1$. - Exercise 2: (a) no; (b) no; (c) $y=-1$; (d) $y=5,-1,-2$; (e) max $9$ at $5$, min $-2$ at $0$. - Exercise 3: (a) yes; (b) yes; (c) no; (d) no. - Exercise 4: (a) $f$ domain all real except $-1$, $g$ all real. (b) $f$ and $g$ domain $[0, \infty)$.