Let's examine the table of values for the function step by step.
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-6 & 8 \\
\hline
7 & 3 \\
\hline
4 & -5 \\
\hline
3 & -2 \\
\hline
-5 & 12 \\
\hline
\end{array}
\][/tex]
1. The ordered pair given in the first row of the table can be written using function notation as [tex]\( f(-6) = 8 \)[/tex].
- The input [tex]\( x = -6 \)[/tex] corresponds to [tex]\( f(-6) \)[/tex].
- The output or the value of the function at [tex]\( x = -6 \)[/tex] is [tex]\( 8 \)[/tex].
2. [tex]\( f(3) \)[/tex] is
- We need to find the value in the second column when [tex]\( x = 3 \)[/tex].
- From the table, when [tex]\( x = 3 \)[/tex], the value corresponding to [tex]\( f(3) \)[/tex] is [tex]\( -2 \)[/tex].
- So, [tex]\( f(3) = -2 \)[/tex].
3. [tex]\( f(x) = -5 \)[/tex] when [tex]\( x \)[/tex] is
- We need to find the value in the first column when [tex]\( f(x) = -5 \)[/tex].
- From the table, the value of [tex]\( x \)[/tex] when [tex]\( f(x) = -5 \)[/tex] is [tex]\( 4 \)[/tex].
- So, [tex]\( f(x) = -5 \)[/tex] when [tex]\( x = 4 \)[/tex].
Putting it all together:
- The ordered pair given in the first row of the table can be written using function notation as [tex]\( f(-6) = 8 \)[/tex].
- [tex]\( f(3) \)[/tex] is [tex]\( -2 \)[/tex].
- [tex]\( f(x) = -5 \)[/tex] when [tex]\( x = 4 \)[/tex].
