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

Question

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 \( x = 2\), \( y = 8 \)