Answered

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}



Answer :

GinnyAnswer
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.

Other Questions