Question

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

Answer 1

To demonstrate that the function \( y = \frac{1}{2}f(x) \) results in a vertical compression of the parent function \( y = f(x) = x^4 \) when \( k = \frac{1}{2} \), we will complete the second table (for \( y = \frac{1}{2}x^4 \)) based on the values from the first table.

### Parent Function Table (y = x^4)

| x | y = x^4 |
|-----|-----------|
| 0 | 0 |
| 1 | 1 |
| 2 | 16 |

### Compressed Function Table (y = 1/2 x^4)

To calculate the values for the second table, we will take the values from the first table and multiply them by \(\frac{1}{2}\):

- For \( x = 0 \): \( y = \frac{1}{2} \cdot 0^4 = \frac{1}{2} \cdot 0 = 0 \)
- For \( x = 1 \): \( y = \frac{1}{2} \cdot 1^4 = \frac{1}{2} \cdot 1 = \frac{1}{2} \)
- For \( x = 2 \): \( y = \frac{1}{2} \cdot 2^4 = \frac{1}{2} \cdot 16 = 8 \)

### Complete Compressed Function Table (y = 1/2 x^4)

| x | y = 1/2 x^4 |
|-----|---------------|
| 0 | 0 |
| 1 | 0.5 |
| 2 | 8 |

### Summary:
- At \( x=0 \), \( y=0 \) remains the same.
- At \( x=1 \), \( y=1 \) is vertically compressed to \( y=0.5 \).
- At \( x=2 \), \( y=16 \) is vertically compressed to \( y=8 \).

This confirms that the function \( y = \frac{1}{2}x^4 \) is a vertically compressed version of the parent function \( y = x^4 \).