1. **Problem Statement:** Given two functions $f(x)$ and $g(x)$ with their graphs, we need to sketch the graph of $h(x) = f(x) - g(x)$. 2. **Understanding the functions:** - $f(x)$ is a line passing through points $(-1,-1)$, $(0,0)$, and $(1,1)$. - $g(x)$ is a curve passing through points $(0,1)$, $(1,0)$, and $(2,-2)$. 3. **Formula for $h(x)$:** $$h(x) = f(x) - g(x)$$ 4. **Calculate $h(x)$ at key points:** - At $x=-1$: $f(-1) = -1$, $g(-1)$ is not given, so we cannot calculate $h(-1)$. - At $x=0$: $f(0) = 0$, $g(0) = 1$, so $$h(0) = 0 - 1 = -1$$ - At $x=1$: $f(1) = 1$, $g(1) = 0$, so $$h(1) = 1 - 0 = 1$$ - At $x=2$: $f(2)$ is not given, but assuming $f(x)$ is linear with slope 1 (from points), $$f(2) = 2$$ $g(2) = -2$, so $$h(2) = 2 - (-2) = 4$$ 5. **Plotting points for $h(x)$:** - $(0, -1)$ - $(1, 1)$ - $(2, 4)$ 6. **Sketching $h(x)$:** Since $f(x)$ is linear with slope 1, and $g(x)$ is a curve, $h(x)$ will be the vertical difference between $f(x)$ and $g(x)$ at each $x$. 7. **Summary:** The graph of $h(x)$ passes through points $(0,-1)$, $(1,1)$, and $(2,4)$ and can be sketched by connecting these points smoothly, reflecting the subtraction of $g(x)$ from $f(x)$. **Final answer:** $$h(x) = f(x) - g(x)$$ with key points $(0,-1)$, $(1,1)$, $(2,4)$ for sketching.