Let's work through the steps to determine the values of the function [tex]\( f(x) \)[/tex] for the given points.
Here is the data presented in tabular form:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-1 & 2 \frac{2}{3} \\
\hline
0 & 2 \\
\hline
1 & 0 \\
\hline
2 & -6 \\
\hline
3 & -24 \\
\hline
\end{array}
\][/tex]
### Step-by-Step Solution:
1. Interpret the Fractional Value:
- For [tex]\( x = -1 \)[/tex], [tex]\( f(x) = 2 \frac{2}{3} \)[/tex].
- We need to convert the mixed number [tex]\( 2 \frac{2}{3} \)[/tex] into an improper fraction or a decimal.
- [tex]\( 2 \frac{2}{3} \)[/tex] can be written as [tex]\( 2 + \frac{2}{3} \)[/tex].
- Converting [tex]\( 2 \frac{2}{3} \)[/tex] to a decimal: [tex]\( 2 + \frac{2}{3} = 2 + 0.6666666666666666 \approx 2.6666666666666665 \)[/tex].
2. Write Down the Points:
Now we have the following points and their corresponding function values:
- For [tex]\( x = -1 \)[/tex], [tex]\( f(x) \approx 2.6666666666666665 \)[/tex].
- For [tex]\( x = 0 \)[/tex], [tex]\( f(x) = 2 \)[/tex].
- For [tex]\( x = 1 \)[/tex], [tex]\( f(x) = 0 \)[/tex].
- For [tex]\( x = 2 \)[/tex], [tex]\( f(x) = -6 \)[/tex].
- For [tex]\( x = 3 \)[/tex], [tex]\( f(x) = -24 \)[/tex].
3. Summarize the Points:
We can summarize the points in a compact form:
[tex]\[
\begin{align*}
(-1, & \, 2.6666666666666665) \\
(0, & \, 2) \\
(1, & \, 0) \\
(2, & \, -6) \\
(3, & \, -24)
\end{align*}
\][/tex]
### Summary
The values of the function [tex]\( f(x) \)[/tex] for the given points are:
[tex]\[
[(-1, 2.6666666666666665), (0, 2), (1, 0), (2, -6), (3, -24)]
\][/tex]
This tabulation helps us understand the behavior of the function at these specific points.
