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Problem 10

aCompute the missing values in the following table and supply a valid technology formula for the given function: HINT [See Quick Examples on page 633.] $$ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \boldsymbol{x} & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & & & & & & & \\ \hline \end{array} $$ \(r(x)=2^{-x}+1\)

Expert verified

The missing values in the table are obtained by evaluating the function \(r(x) = 2^{-x} + 1\) at the given x values: \(r(-3) = 9\), \(r(-2) = 5\), \(r(-1) = 3\), \(r(0) = 2\), \(r(1) = \frac{3}{2}\), \(r(2) = \frac{5}{4}\), and \(r(3) = \frac{9}{8}\). The completed table is:
$$
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline \boldsymbol{x} & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline \boldsymbol{f}(\boldsymbol{x}) & 9 & 5 & 3 & 2 & \frac{3}{2} & \frac{5}{4} & \frac{9}{8} \\
\hline
\end{array}
$$

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Chapter 9

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