1. **State the problem:** We are given two functions $f(x)$ and $h(x)$ with their values at $x = -2, -1, 0, 1, 2$. We want to express $h(x)$ as a transformation of $f(x)$. 2. **List the given values:** - $f(-2) = 0$, $f(-1) = -1$, $f(0) = 2$, $f(1) = -2$, $f(2) = -4$ - $h(-2) = -2$, $h(-1) = -3$, $h(0) = 0$, $h(1) = -4$, $h(2) = -6$ 3. **Check if $h(x)$ is a vertical shift of $f(x)$:** Calculate $h(x) - f(x)$ for each $x$: - $h(-2) - f(-2) = -2 - 0 = -2$ - $h(-1) - f(-1) = -3 - (-1) = -2$ - $h(0) - f(0) = 0 - 2 = -2$ - $h(1) - f(1) = -4 - (-2) = -2$ - $h(2) - f(2) = -6 - (-4) = -2$ Since $h(x) - f(x) = -2$ for all $x$, this means $h(x) = f(x) - 2$. 4. **Check other options for completeness:** - $f(x) + 2$ would add 2, not subtract. - $f(x + 2)$ and $f(x - 2)$ represent horizontal shifts, which would change the $x$ values where function values appear, but the $x$ values are the same in both tables. 5. **Conclusion:** The correct transformation is $$h(x) = f(x) - 2$$ This means $h(x)$ is the function $f(x)$ shifted downward by 2 units.