To solve the given problem, we need to apply the function [tex]\( f(x) = \frac{1}{4} x \)[/tex] to each value of [tex]\( x \)[/tex] and find the corresponding [tex]\( y \)[/tex] values. Let's do this step by step for each [tex]\( x \)[/tex] value provided.
For [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = \frac{1}{4} \times 1 = 0.25 \][/tex]
So, [tex]\( y = 0.25 \)[/tex] when [tex]\( x = 1 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = \frac{1}{4} \times 2 = 0.5 \][/tex]
So, [tex]\( y = 0.5 \)[/tex] when [tex]\( x = 2 \)[/tex].
For [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = \frac{1}{4} \times 3 = 0.75 \][/tex]
So, [tex]\( y = 0.75 \)[/tex] when [tex]\( x = 3 \)[/tex].
For [tex]\( x = 4 \)[/tex]:
[tex]\[ f(4) = \frac{1}{4} \times 4 = 1.0 \][/tex]
So, [tex]\( y = 1.0 \)[/tex] when [tex]\( x = 4 \)[/tex].
For [tex]\( x = 5 \)[/tex]:
[tex]\[ f(5) = \frac{1}{4} \times 5 = 1.25 \][/tex]
So, [tex]\( y = 1.25 \)[/tex] when [tex]\( x = 5 \)[/tex].
Now, we can fill the table with the calculated [tex]\( y \)[/tex] values:
[tex]\[
\begin{tabular}{|l|l|l|l|l|l|}
\hline
$x$ & 1 & 2 & 3 & 4 & 5 \\
\hline
$y$ & 0.25 & 0.5 & 0.75 & 1.0 & 1.25 \\
\hline
\end{tabular}
\][/tex]
