To determine the information about the continuous function that generated the given table of values, let's analyze the data carefully.
The given table of values is as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0.125 & -3 \\
\hline
0.5 & -1 \\
\hline
2 & 1 \\
\hline
8 & 3 \\
\hline
64 & 6 \\
\hline
\end{array}
\][/tex]
To find out whether the function has any [tex]$x$[/tex]-intercepts, we need to observe where the value of [tex]\( y \)[/tex] is equal to [tex]\( 0 \)[/tex]. An [tex]$x$[/tex]-intercept occurs where the function crosses the x-axis, that is where the output [tex]\( y \)[/tex] is zero.
Checking the [tex]\( y \)[/tex]-values from the table:
- At [tex]\( x = 0.125 \)[/tex], [tex]\( y = -3 \)[/tex]
- At [tex]\( x = 0.5 \)[/tex], [tex]\( y = -1 \)[/tex]
- At [tex]\( x = 2 \)[/tex], [tex]\( y = 1 \)[/tex]
- At [tex]\( x = 8 \)[/tex], [tex]\( y = 3 \)[/tex]
- At [tex]\( x = 64 \)[/tex], [tex]\( y = 6 \)[/tex]
We observe that none of the [tex]\( y \)[/tex]-values are equal to zero ([tex]\( y = 0 \)[/tex]). This means that for the given set of values in the table, the function does not cross the x-axis at any point.
Therefore, it can be concluded that:
B. the function has no [tex]\( x \)[/tex]-intercepts
