Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Which table represents the second piece of the function [tex]$f(x)=\left\{\begin{array}{ll}-3.5x+0.5, & x\ \textless \ 1 \\ 8-2x, & x \geq 1\end{array}\right.$[/tex]?

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
-1 & 4 \\
\hline
0 & 0.5 \\
\hline
1 & -3 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
-1 & 10 \\
\hline
0 & 8 \\
\hline
1 & 6 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
1 & 6 \\
\hline
2 & 4 \\
\hline
3 & 2 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
1 & -3 \\
\hline
2 & -6.5 \\
\hline
3 & -10 \\
\hline
\end{tabular}


Sagot :

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.