1. **State the problem:** We are given a function $g(x)$ defined on the interval $-2 \leq x \leq 3$ and asked to find specific values and transformations based on its graph. 2. **Part (a): Find $g(3)$** - From the graph, locate the point where $x=3$. - The corresponding $y$-value is the value of $g(3)$. - According to the problem, $g(3) = 2$. 3. **Part (b): Find $x$ such that $g(x) = 1$** - Look for points on the graph where the $y$-value is 1. - From the graph, this occurs at $x = -1$. 4. **Part (c): Draw the graph of $y = g(x) - 2$** - The transformation $y = g(x) - 2$ shifts the original graph down by 2 units. - For each point $(x, g(x))$ on the original graph, the new point is $(x, g(x) - 2)$. - For example, the endpoint at $(-2, 0)$ moves to $(-2, 0 - 2) = (-2, -2)$. - The peak at $(1, 3)$ moves to $(1, 3 - 2) = (1, 1)$. - The endpoint at $(3, 2)$ moves to $(3, 2 - 2) = (3, 0)$. This explains how the answers are obtained from the graph and the transformation.