To determine the number of zeros indicated by the values in the table representing the graph of a continuous function, we need to find the points where the function's value [tex]\( y \)[/tex] is equal to zero. These points are the x-values where the corresponding y-values are zero in the table.
Let's look at the table entries:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-3.0 & 8.40 \\
\hline
-2.4 & 0.69 \\
\hline
-1.8 & -0.39 \\
\hline
-1.2 & 0.24 \\
\hline
-0.6 & 0.46 \\
\hline
0 & 0 \\
\hline
0.6 & -0.46 \\
\hline
1.2 & -0.24 \\
\hline
1.8 & 0.39 \\
\hline
2.4 & -0.69 \\
\hline
3.0 & -8.40 \\
\hline
\end{array}
\][/tex]
From the table, we observe that the value of [tex]\( y \)[/tex] is zero at [tex]\( x = 0 \)[/tex]. This means that the function crosses the x-axis at this point.
Therefore, the continuous function represented by the given table of values has one zero.
The x-value at which this function has a zero is at [tex]\( x = 0 \)[/tex] where [tex]\( y = 0 \)[/tex].
So, the number of zeros is [tex]\( 1 \)[/tex] and the positions of the zeros are [tex]\((0, 0)\)[/tex].
