1. The problem is to find the expression for the function $$y = -2 f(1 - x) + 2$$ given the points of the original function $f(x)$: $(-2, 3)$, $(-1, 0)$, $(0, 1)$, and $(1, 0)$.\n\n2. We start by understanding the transformation inside the function: $f(1 - x)$ means the function $f$ is reflected and shifted horizontally. Specifically, the input $x$ is replaced by $1 - x$.\n\n3. Next, the function is multiplied by $-2$, which reflects it vertically and stretches it by a factor of 2.\n\n4. Finally, we add 2 to the entire function, which shifts it vertically upward by 2 units.\n\n5. To find the new points for $y = -2 f(1 - x) + 2$, we calculate $f(1 - x)$ for each $x$ and then apply the transformations:\n\n- For $x = -2$: $1 - (-2) = 3$. Since $f(3)$ is not given, we cannot find this point exactly.\n- For $x = -1$: $1 - (-1) = 2$. $f(2)$ is not given.\n- For $x = 0$: $1 - 0 = 1$. $f(1) = 0$ from the original points.\n- For $x = 1$: $1 - 1 = 0$. $f(0) = 1$.\n\n6. Using the known points:\n- At $x=0$: $y = -2 imes f(1) + 2 = -2 imes 0 + 2 = 2$\n- At $x=1$: $y = -2 imes f(0) + 2 = -2 imes 1 + 2 = 0$\n\n7. Since we only have partial data, the transformed function is defined by these points and the transformations described.\n\n8. The function can be expressed as $$y = -2 f(1 - x) + 2$$ where $f(x)$ is the piecewise linear function passing through $(-2,3)$, $(-1,0)$, $(0,1)$, and $(1,0)$.