1. **State the problem:** We are given the linear function $$y = -2x - 1$$ and a table with some known and unknown values: $$\begin{array}{c|ccccc} x & -2 & -1 & 0 & 1 & 2 \\ y & 3 & A & B & -3 & C \\\end{array}$$ We need to find the values of A, B, and C. 2. **Recall the formula:** The function is linear, so for any value of $x$, the corresponding $y$ is given by: $$y = -2x - 1$$ 3. **Calculate A:** When $x = -1$, $$y = -2(-1) - 1 = 2 - 1 = 1$$ So, $$A = 1$$. 4. **Calculate B:** When $x = 0$, $$y = -2(0) - 1 = 0 - 1 = -1$$ So, $$B = -1$$. 5. **Calculate C:** When $x = 2$, $$y = -2(2) - 1 = -4 - 1 = -5$$ So, $$C = -5$$. 6. **Verify given values:** For $x = -2$, $$y = -2(-2) - 1 = 4 - 1 = 3$$ which matches the table value 3. For $x = 1$, $$y = -2(1) - 1 = -2 - 1 = -3$$ which matches the table value -3. **Final answers:** $$A = 1, \quad B = -1, \quad C = -5$$