Let's address the given table of values for the function [tex]\( y = \frac{1}{x} \)[/tex].
We are given:
[tex]\[
\begin{tabular}{c|c|c|c|c|c}
$x$ & 0 & 1 & 2 & 4 & 8 \\
\hline
$y$ & undefined & 1 & A & 0.25 & B \\
\end{tabular}
\][/tex]
To fill in the missing values for [tex]\( y \)[/tex], we need to evaluate [tex]\( \frac{1}{x} \)[/tex] at the corresponding [tex]\( x \)[/tex]-values:
1. When [tex]\( x = 0 \)[/tex]:
- [tex]\( y = \frac{1}{0} \)[/tex] is undefined.
2. When [tex]\( x = 1 \)[/tex]:
- [tex]\( y = \frac{1}{1} = 1 \)[/tex].
3. When [tex]\( x = 2 \)[/tex]:
- [tex]\( y = \frac{1}{2} \)[/tex].
- Thus, [tex]\( A = 0.5 \)[/tex].
4. When [tex]\( x = 4 \)[/tex]:
- [tex]\( y = \frac{1}{4} = 0.25 \)[/tex].
5. When [tex]\( x = 8 \)[/tex]:
- [tex]\( y = \frac{1}{8} \)[/tex].
- Thus, [tex]\( B = 0.125 \)[/tex].
Now, substituting the calculated values into the table, we have:
[tex]\[
\begin{tabular}{c|c|c|c|c|c}
$x$ & 0 & 1 & 2 & 4 & 8 \\
\hline
$y$ & undefined & 1 & 0.5 & 0.25 & 0.125 \\
\end{tabular}
\][/tex]
Therefore, the values that replace [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are:
[tex]\[
A = 0.5 \quad \text{and} \quad B = 0.125
\][/tex]
