1. The problem involves analyzing a given graph of a function $f$ and answering questions about values, domain, range, and intervals of increase. 2. (a) To find $f(-1)$, locate $x = -1$ on the graph and read the corresponding $y$-value. 3. (b) To estimate $f(2)$, find $x = 2$ on the graph and approximate the $y$-value. 4. (c) To find $x$ such that $f(x) = 2$, look for points where the graph crosses the horizontal line $y = 2$. 5. (d) To estimate $x$ values where $f(x) = 0$, find where the graph crosses the $x$-axis. 6. (e) The domain is all $x$-values for which the function is defined (visible on the graph). 7. The range is all $y$-values the function attains. 8. (f) The function is increasing where the graph goes upward as $x$ increases. --- **Step-by-step answers:** 1. (a) At $x = -1$, the graph shows $f(-1) \approx 2$ (since the curve starts from the top left near $y=2$). 2. (b) At $x = 2$, the graph is slightly above $y=1$, so $f(2) \approx 1.2$. 3. (c) $f(x) = 2$ at $x = -1$ (from part a) and also near $x = 3$ where the graph rises past $y=2$. 4. (d) $f(x) = 0$ where the graph crosses the $x$-axis, approximately between $x=0.5$ and $x=1$. 5. (e) Domain: The graph is shown from about $x = -1$ to $x = 3$, so domain is $[-1, 3]$. Range: The lowest point is below $y=0$ (negative), and the highest is about $y=2$, so range is approximately $[-0.5, 2]$. 6. (f) The function is increasing on the interval approximately $[1, 3]$ where the graph rises. --- **Final answers:** - $f(-1) = 2$ - $f(2) \approx 1.2$ - $f(x) = 2$ at $x = -1$ and near $x = 3$ - $f(x) = 0$ near $x = 0.5$ to $1$ - Domain: $[-1, 3]$ - Range: $[-0.5, 2]$ - Increasing on $[1, 3]$