To find the maximum value of the function [tex]\( f(x) \)[/tex] given the values in the table, we follow these steps:
1. Identify all the [tex]\(f(x)\)[/tex] values provided in the table.
2. Compare these values to determine the maximum.
From the table, the [tex]\(f(x)\)[/tex] values are:
[tex]\[
-7, 0, 5, 8, 8, 5, 0, -7
\][/tex]
Next, we look for the highest value among these:
- The value [tex]\(-7\)[/tex] appears at [tex]\(x = -5\)[/tex] and [tex]\(x = 3\)[/tex].
- The value [tex]\(0\)[/tex] appears at [tex]\(x = -4\)[/tex] and [tex]\(x = 2\)[/tex].
- The value [tex]\(5\)[/tex] appears at [tex]\(x = -3\)[/tex] and [tex]\(x = 1\)[/tex].
- The value [tex]\(8\)[/tex] appears at [tex]\(x = -2\)[/tex] and [tex]\(x = 0\)[/tex].
Comparing all these values, we see that the maximum value is:
[tex]\[
8
\][/tex]
Therefore, the maximum value of [tex]\(f(x)\)[/tex] is:
[tex]\[
\boxed{8}
\][/tex]
Now, assuming we need to compare this to another function [tex]\(g(x)\)[/tex], the problem asks us to complete the statement:
The maximum value of [tex]\(f(x)\)[/tex] is [tex]\(\square\)[/tex] the maximum value of [tex]\(g(x)\)[/tex].
Since we haven’t been provided with the values of [tex]\(g(x)\)[/tex], we can’t complete the comparative statement accurately. However, given the specific solution process described, it is reasonable to confidently say that:
“The maximum value of [tex]\( f(x) \)[/tex] is 8.”
To complete the drop-down statement for the given maximum:
```
The maximum value of [tex]\( f(x) \)[/tex] is equal to 8.
```
This matches the maximal findings within the provided [tex]\( f(x) \)[/tex] dataset.
