Question

Complete the table to show that y=kf(x) results in the parent function being vertically compressed when k=1/2
x y =x^4
0 0
1 1
2 16

x y=1/2x^4
0 0
1 __
2 ___

Answer 1

To complete the table for the function \( y = \frac{1}{2}x^4 \), we can calculate the values by substituting \( x \) into the equation.

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

2. When \( x = 2 \):
\[
y = \frac{1}{2}(2^4) = \frac{1}{2}(16) = 8
\]

Now, filling in the completed table:

\[
\begin{array}{|c|c|c|}
\hline
x & y = x^4 & y = \frac{1}{2}x^4 \\
\hline
0 & 0 & 0 \\
1 & 1 & \frac{1}{2} \\
2 & 16 & 8 \\
\hline
\end{array}
\]

So, for the function \( y = \frac{1}{2}x^4 \):
- When \( x = 1\), \( y = \frac{1}{2} \)
- When \( x = 2\), \( y = 8 \)