Let's analyze the given function and the transformation step-by-step.
We are given the function \( f \) represented in a table of values:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 \\
\hline
f(x) & 13 & 19 & 37 & 91 & 253 \\
\hline
\end{array}
\][/tex]
First, we need to determine the effect of translating the function \( f \) down by 4 units. Translating a function \( f \) vertically down by 4 units means subtracting 4 from each \( f(x) \) value.
Let's find the translated values:
- \( f(1) = 13 \) will become \( 13 - 4 = 9 \)
- \( f(2) = 19 \) will become \( 19 - 4 = 15 \)
- \( f(3) = 37 \) will become \( 37 - 4 = 33 \)
- \( f(4) = 91 \) will become \( 91 - 4 = 87 \)
- \( f(5) = 253 \) will become \( 253 - 4 = 249 \)
Therefore, the points for the transformed function would be:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 \\
\hline
f(x) - 4 & 9 & 15 & 33 & 87 & 249 \\
\hline
\end{array}
\][/tex]
Now, we need to select an example point from the transformed function's table and insert it into the appropriate position.
Given the transformed values, we can select any point. Let's use \( x = 2 \) as an example.
For \( x = 2 \), the value in the transformed function \( f(x) - 4 \) is \( 15 \). Hence, the point is \( (2, 15) \).
Therefore, the correct completion of the statements would be:
1. The parent function of the function represented in the table is \( f(x) \).
2. If function \( f \) was translated down 4 units, the \( y \)-values would be decreased by 4 units each.
3. A point in the table for the transformed function would be [tex]\( (2, 15) \)[/tex].
