Let's break down the given question step by step:
1. Understanding the Function Table:
We are provided a table that represents a function [tex]\( f(x) \)[/tex], where [tex]\( x \)[/tex] is the input and [tex]\( f(x) \)[/tex] is the output.
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & f(x) \\
\hline
2 & 6 \\
\hline
7 & 3 \\
\hline
9 & 5 \\
\hline
\end{tabular}
\][/tex]
From this table, we can see that:
- [tex]\( f(2) = 6 \)[/tex]
- [tex]\( f(7) = 3 \)[/tex]
- [tex]\( f(9) = 5 \)[/tex]
2. Writing the Ordered Pair Using Function Notation:
The question asks us to write the ordered pair given in the bottom row using function notation. From the bottom row of our table, we see that when [tex]\( x = 9 \)[/tex], [tex]\( f(x) = 5 \)[/tex].
So, the ordered pair (9, 5) can be written in function notation as:
[tex]\[
f(9) = 5
\][/tex]
3. Evaluating [tex]\( I(5, 9) \)[/tex]:
We are given that [tex]\( I(5, 9) = 14 \)[/tex]. This seems to be a calculated result based on specific instructions or conditions not detailed here, but we accept this given value as accurate. Hence:
[tex]\[
I(5, 9) = 14
\][/tex]
4. Summary and Conclusion:
- From the function table, [tex]\( f(9) = 5 \)[/tex].
- It has been given that [tex]\( I(5, 9) = 14 \)[/tex].
So, the detailed step-by-step solution of the problem is:
- From the table, we determined [tex]\( f(9) = 5 \)[/tex].
- We noted that it is given [tex]\( I(5, 9) = 14 \)[/tex].
Hence, the final answers are:
- [tex]\( f(9) = 5 \)[/tex]
- [tex]\( I(5, 9) = 14 \)[/tex]
