Let's solve the given problem step-by-step. We need to determine the values of [tex]\( f(x) \)[/tex] for each corresponding [tex]\( x \)[/tex] in the table.
The given values are:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 \\
\hline
f(x) & -50 & -25 & -\frac{25}{2} & -\frac{25}{4} \\
\hline
\end{array}
\][/tex]
### Step-by-Step Calculation
1. For [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = -50
\][/tex]
So, the first entry in the solution is:
[tex]\[
(0, -50)
\][/tex]
2. For [tex]\( x = 1 \)[/tex]:
[tex]\[
f(1) = -25
\][/tex]
So, the second entry in the solution is:
[tex]\[
(1, -25)
\][/tex]
3. For [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = -\frac{25}{2}
\][/tex]
Simplifying [tex]\( -\frac{25}{2} \)[/tex] to a decimal gives us:
[tex]\[
f(2) = -12.5
\][/tex]
So, the third entry in the solution is:
[tex]\[
(2, -12.5)
\][/tex]
4. For [tex]\( x = 3 \)[/tex]:
[tex]\[
f(3) = -\frac{25}{4}
\][/tex]
Simplifying [tex]\( -\frac{25}{4} \)[/tex] to a decimal gives us:
[tex]\[
f(3) = -6.25
\][/tex]
So, the fourth entry in the solution is:
[tex]\[
(3, -6.25)
\][/tex]
### Final Table
Combining all these results, we form the resultant table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & -50 \\
1 & -25 \\
2 & -12.5 \\
3 & -6.25 \\
\hline
\end{array}
\][/tex]
Thus, the solution can be summarized as the set of pairs [tex]\((x, f(x))\)[/tex]:
[tex]\[
[(0, -50), (1, -25), (2, -12.5), (3, -6.25)]
\][/tex]
These pairs represent the values of [tex]\( f(x) \)[/tex] for the given [tex]\( x \)[/tex] values.
