To identify the table that represents the second piece of the function \( f(x) \), defined as:
[tex]\[ f(x) = \left\{
\begin{array}{ll}
-3.5x + 0.5, & \text{ for } x < 1 \\
8 - 2x, & \text{ for } x \geq 1
\end{array}
\right. \][/tex]
we will evaluate the second part of this piecewise function for \( x \geq 1 \), at several integer values of \( x \).
### Evaluating \( f(x) = 8 - 2x \):
1. For \( x = 1 \):
[tex]\[
f(1) = 8 - 2(1) = 8 - 2 = 6
\][/tex]
2. For \( x = 2 \):
[tex]\[
f(2) = 8 - 2(2) = 8 - 4 = 4
\][/tex]
3. For \( x = 3 \):
[tex]\[
f(3) = 8 - 2(3) = 8 - 6 = 2
\][/tex]
Now that we have evaluated the function, we can compile the results into a table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
1 & 6 \\
\hline
2 & 4 \\
\hline
3 & 2 \\
\hline
\end{array}
\][/tex]
Hence, the table representing the second piece of the function \( f(x) = 8 - 2x \) for \( x \geq 1 \) is:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
1 & 6 \\
\hline
2 & 4 \\
\hline
3 & 2 \\
\hline
\end{array}
\][/tex]
This corresponds to the third table provided in the question.
