1. **State the problem:** We are given the function $y = 2x + 2$ and need to fill in the table values for $x = -3, -2, -1, 0, 1, 2, 3$ by computing $2x$ and then $y$ using the formula. 2. **Formula used:** The function is $y = 2x + 2$. For each $x$, first calculate $2x$, then add 2 to get $y$. 3. **Calculate values column by column:** - For $x = -3$: $2x = 2 \times (-3) = -6$, then $y = -6 + 2 = -4$ - For $x = -2$: $2x = 2 \times (-2) = -4$, then $y = -4 + 2 = -2$ - For $x = -1$: $2x = 2 \times (-1) = -2$, then $y = -2 + 2 = 0$ - For $x = 0$: $2x = 2 \times 0 = 0$, then $y = 0 + 2 = 2$ - For $x = 1$: $2x = 2 \times 1 = 2$, then $y = 2 + 2 = 4$ - For $x = 2$: $2x = 2 \times 2 = 4$, then $y = 4 + 2 = 6$ - For $x = 3$: $2x = 2 \times 3 = 6$, then $y = 6 + 2 = 8$ 4. **Completed table:** | x | 2x | y = 2x + 2 | |----|----|------------| | -3 | -6 | -4 | | -2 | -4 | -2 | | -1 | -2 | 0 | | 0 | 0 | 2 | | 1 | 2 | 4 | | 2 | 4 | 6 | | 3 | 6 | 8 | 5. **Explanation:** For each $x$ value, multiply by 2 to get $2x$, then add 2 to find $y$. This linear function increases by 2 for each increase of 1 in $x$. Final answer: The table is filled as above.