Function Shift D0F7A1

1. **State the problem:** We are given a function $f$ with values at certain $x$ points and a transformed function $g$ defined by $g(x) = f(x - 4)$. We need to create a table for $g(x)$ based on the given $f(x)$ values. 2. **Understand the transformation:** The function $g(x) = f(x - 4)$ represents a horizontal shift of the function $f$ to the right by 4 units. This means to find $g(x)$ at a particular $x$, we evaluate $f$ at $x - 4$. 3. **Given values:** - For $x = -1, 0, 1, 2$, the values of $f(x)$ are $-4, -3, -2, -1$ respectively. 4. **Calculate $g(x)$ for each $x$ in the table:** - $g(-1) = f(-1 - 4) = f(-5)$, but $f(-5)$ is not given, so $g(-1)$ is undefined or unknown. - $g(0) = f(0 - 4) = f(-4)$, $f(-4)$ is not given, so $g(0)$ is undefined. - $g(1) = f(1 - 4) = f(-3)$, $f(-3)$ is not given, so $g(1)$ is undefined. - $g(2) = f(2 - 4) = f(-2)$, $f(-2)$ is not given, so $g(2)$ is undefined. 5. **Since $f(x)$ values are only given for $x = -1, 0, 1, 2$, we cannot find $g(x)$ for these $x$ values directly.** 6. **Instead, find $g(x)$ values for $x$ such that $x - 4$ is in the domain of $f$ (i.e., $-1, 0, 1, 2$):** - Let $x - 4 = -1 ightarrow x = 3$, so $g(3) = f(-1) = -4$ - Let $x - 4 = 0 ightarrow x = 4$, so $g(4) = f(0) = -3$ - Let $x - 4 = 1 ightarrow x = 5$, so $g(5) = f(1) = -2$ - Let $x - 4 = 2 ightarrow x = 6$, so $g(6) = f(2) = -1$ 7. **Create the table for $g(x)$:** | $x$ | 3 | 4 | 5 | 6 | |-----|---|---|---|---| | $g(x)$ | $-4$ | $-3$ | $-2$ | $-1$ | 8. **Summary:** The function $g$ is the function $f$ shifted 4 units to the right, so the $x$ values for $g$ are shifted by 4 compared to $f$.