Question

Complete the tables to show that y=kf(x) results in the parent function being vertically compressed when k=12.(1 point)
x y=x4
0 0
1 1
2 16
x y=12x4
0 0
1
2

Answer 1

To show that the function \( y = kf(x) \) results in the parent function being vertically compressed when \( k = \frac{1}{12} \), we start with the function \( y = x^4 \) and then apply the compression factor \( k = \frac{1}{12} \).

Given the parent function \( y = x^4 \):

\[
\begin{array}{|c|c|}
\hline
x & y = x^4 \\
\hline
0 & 0 \\
1 & 1 \\
2 & 16 \\
\hline
\end{array}
\]

Now, let’s calculate \( y = \frac{1}{12} x^4 \):

1. For \( x = 0 \):
\[
y = \frac{1}{12} \cdot 0^4 = 0
\]

2. For \( x = 1 \):
\[
y = \frac{1}{12} \cdot 1^4 = \frac{1}{12}
\]

3. For \( x = 2 \):
\[
y = \frac{1}{12} \cdot 2^4 = \frac{1}{12} \cdot 16 = \frac{16}{12} = \frac{4}{3} \approx 1.33
\]

Now, we can complete the table for \( y = \frac{1}{12} x^4 \):

\[
\begin{array}{|c|c|}
\hline
x & y = \frac{1}{12} x^4 \\
\hline
0 & 0 \\
1 & \frac{1}{12} \\
2 & \frac{4}{3} \\
\hline
\end{array}
\]

So, summarizing the completed tables:

### Parent Function \( y = x^4 \)
\[
\begin{array}{|c|c|}
\hline
x & y = x^4 \\
\hline
0 & 0 \\
1 & 1 \\
2 & 16 \\
\hline
\end{array}
\]

### Compressed Function \( y = \frac{1}{12} x^4 \)
\[
\begin{array}{|c|c|}
\hline
x & y = \frac{1}{12} x^4 \\
\hline
0 & 0 \\
1 & \frac{1}{12} \\
2 & \frac{4}{3} \\
\hline
\end{array}
\]

This shows that the output values for \( y = \frac{1}{12} x^4 \) are less than those for \( y = x^4 \), confirming that the function \( y = \frac{1}{12} x^4 \) is a vertical compression of the parent function \( y = x^4 \).