1. **State the problem:** We are given a function $y = f(x)$ represented by points $(-3, 2), (-2, 4), (-1, 2)$ forming a "tent" shape. We need to find the transformed function $h(x) = -f(x - 3) + 5$ and describe how the graph changes. 2. **Understand the transformation:** The function $h(x) = -f(x - 3) + 5$ involves three transformations: - Horizontal shift right by 3 units (replace $x$ by $x-3$). - Reflection about the x-axis (multiply the function by $-1$). - Vertical shift up by 5 units (add 5). 3. **Apply transformations to each point:** - Original points: $(-3, 2), (-2, 4), (-1, 2)$. - Shift $x$ by 3: new $x$ values are $-3+3=0$, $-2+3=1$, $-1+3=2$. - Evaluate $f(x-3)$ at these points: $f(0)=2$, $f(1)=4$, $f(2)=2$ (using original $f$ values at shifted $x$). - Reflect and shift vertically: $h(x) = -f(x-3) + 5$. 4. **Calculate $h(x)$ values:** - At $x=0$: $h(0) = -f(0) + 5 = -2 + 5 = 3$. - At $x=1$: $h(1) = -f(1) + 5 = -4 + 5 = 1$. - At $x=2$: $h(2) = -f(2) + 5 = -2 + 5 = 3$. 5. **Plot and label:** - The transformed graph $h(x)$ has points $(0, 3), (1, 1), (2, 3)$ forming an inverted "tent" shape shifted right and up. **Final answer:** The graph of $h(x) = -f(x - 3) + 5$ is the original graph shifted right by 3 units, reflected over the x-axis, and shifted up by 5 units, with points $(0, 3), (1, 1), (2, 3)$.