Answer
$\begin{array}{|c|r|r|r|r|r|r|r|}
\hline
x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline
r(x) &9 &5 & 3 & 2 & 3/2 & 5/4 & 9/8 \\
\hline
\end{array}$
Technology formula:$\quad 2$^$(-x)+1\quad$ or $\quad (1/2)$^$x+1$
Work Step by Step
$2^{-x}+1=(\displaystyle \frac{1}{2})^{x}+1$
Technology formula:$\quad 2$^$(-x)+1\quad$ or $\quad (1/2)$^$x+1$
$f(-3)=(\displaystyle \frac{1}{2})^{-3}+1=2^{3}+1=9\qquad $tech:$\qquad (1/2)$^$(-3)+1$
$f(-2)=(\displaystyle \frac{1}{2})^{-2}+1=2^{2}+1=5\qquad $tech:$\qquad (1/2)$^$(-2)+1$
$f(-1)=(\displaystyle \frac{1}{2})^{-1}+1=2+1=3\qquad $tech:$\qquad (1/2)$^$(-1)+1$
$f(0)=2^{0}+1=1+1=2 \qquad $tech:$\qquad 2$^$(-x)+1$
$f(1)=2^{-1}+1=\displaystyle \frac{1}{2}+1=\frac{3}{2} \qquad $tech:$\qquad 2$^$(-1)+1$
$f(2)=2^{-2}+1=\displaystyle \frac{1}{2^{2}}+1=\frac{5}{4} \qquad $tech:$\qquad 2$^$(-2)+1$
$f(3)=2^{-3}+1=\displaystyle \frac{1}{2^{3}}+1=\frac{9}{8} \qquad $tech:$\qquad 2$^$(-3)+1$
