1. **State the problem:** We are given the function $y = 2^{x+3}$ and asked to fill in the values of $x+3$ and $y$ for $x$ values from $-5$ to $0$. 2. **Formula and rules:** The function is an exponential function where the exponent is $x+3$. For each $x$, calculate $x+3$ first, then compute $y = 2^{x+3}$. 3. **Calculate values step-by-step:** - For $x = -5$: $x+3 = -5 + 3 = -2$, so $y = 2^{-2} = \frac{1}{2^2} = \frac{1}{4}$. - For $x = -4$: $x+3 = -4 + 3 = -1$, so $y = 2^{-1} = \frac{1}{2}$. - For $x = -3$: $x+3 = -3 + 3 = 0$, so $y = 2^{0} = 1$. - For $x = -2$: $x+3 = -2 + 3 = 1$, so $y = 2^{1} = 2$. - For $x = -1$: $x+3 = -1 + 3 = 2$, so $y = 2^{2} = 4$. - For $x = 0$: $x+3 = 0 + 3 = 3$, so $y = 2^{3} = 8$. 4. **Summary table:** | $x$ | $x+3$ | $y = 2^{x+3}$ | |-----|-------|--------------| | -5 | -2 | $\frac{1}{4}$ | | -4 | -1 | $\frac{1}{2}$ | | -3 | 0 | 1 | | -2 | 1 | 2 | | -1 | 2 | 4 | | 0 | 3 | 8 | This shows how the function grows exponentially as $x$ increases. **Final answer:** $$ \begin{array}{c|c|c} x & x+3 & y=2^{x+3} \\\hline -5 & -2 & \frac{1}{4} \\ -4 & -1 & \frac{1}{2} \\ -3 & 0 & 1 \\ -2 & 1 & 2 \\ -1 & 2 & 4 \\ 0 & 3 & 8 \end{array} $$