1. We are given the function $y = \frac{12}{x}$ where $x \neq 0$, and an incomplete table of values. We need to fill in the missing $y$ values for given $x$ values. 2. Recall that to find $y$, substitute each $x$ into the function: $$y = \frac{12}{x}.$$ 3. Calculate missing $y$ values: - For $x = -1$: $$y = \frac{12}{-1} = -12.$$ - For $x = 1$: $$y = \frac{12}{1} = 12.$$ - For $x = 3$: $$y = \frac{12}{3} = 4.$$ - For $x = 6$: $$y = \frac{12}{6} = 2.$$ 4. Verify the given values for correctness: - $x = -4$, given $y = -6$: Check $$\frac{12}{-4} = -3,$$ which conflicts with given $y$. Possibly a typo. - $x = -3$, given $y = -3$: Check $$\frac{12}{-3} = -4,$$ conflict again. - $x = -2$, given $y = -6$: Check $$\frac{12}{-2} = -6,$$ correct. 5. Likely the table has some incorrect y-values. The correct y-values from the function should be: | x | y = 12/x | |----|----------| | -4 | -3 | | -3 | -4 | | -2 | -6 | | -1 | -12 | | 1 | 12 | | 2 | 6 | | 3 | 4 | | 4 | 3 | | 6 | 2 | Final Answer: $$\begin{array}{c|c} x & y=\frac{12}{x} \\ \hline -4 & -3 \\ -3 & -4 \\ -2 & -6 \\ -1 & -12 \\ 1 & 12 \\ 2 & 6 \\ 3 & 4 \\ 4 & 3 \\ 6 & 2 \end{array}$$