Let's consider the table of values for the function [tex]\( f \)[/tex]:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
2 & 6 \\
\hline
7 & 3 \\
\hline
9 & 5 \\
\hline
\end{tabular}
\][/tex]
The question is about the ordered pair given in the bottom row of the table. The pair from the bottom row is [tex]\( (9, 5) \)[/tex]. We need to express this pair using function notation.
Function notation is a way to represent the value of a function at a specific input. For example, if we have the pair [tex]\( (x, f(x)) \)[/tex], it means that for an input [tex]\( x \)[/tex], the function [tex]\( f \)[/tex] produces the value [tex]\( f(x) \)[/tex].
In the table, the bottom row gives us the pair [tex]\( (9, 5) \)[/tex]. This means that when the input to the function [tex]\( f \)[/tex] is [tex]\( 9 \)[/tex], the output is [tex]\( 5 \)[/tex]. Using function notation, we write this as:
[tex]\[ f(9) = 5 \][/tex]
Now let's examine the provided options:
1. [tex]\( f(9)=5 \)[/tex]
2. [tex]\( f(5)=9 \)[/tex]
3. [tex]\( f(5,9)=14 \)[/tex]
4. [tex]\( f(9,5)=14 \)[/tex]
From the ordered pair [tex]\( (9, 5) \)[/tex], we see that the correct expression using function notation is [tex]\( f(9) = 5 \)[/tex].
Therefore, the correct answer is:
[tex]\[ f(9)=5 \][/tex]
