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 16 2 xy = 1/2 * x ^ 4 0 1 0 2

Answer 1

To show that the function \( y = \frac{1}{2} f(x) \) results in a vertical compression of the parent function \( y = x^4 \), we will complete the tables for both functions.

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

| x | y = x^4 |
|-------|-------------|
| 0 | 0 | (0^4 = 0)
| 1 | 1 | (1^4 = 1)
| 2 | 16 | (2^4 = 16)
| 3 | 81 | (3^4 = 81)

### Vertically Compressed Function Table: \( y = \frac{1}{2} x^4 \)

To find the values of \( y = \frac{1}{2} x^4 \), we can substitute our \( x \) values into the equation.

| x | y = \frac{1}{2} x^4 |
|-------|--------------------------|
| 0 | 0 | (1/2 * 0^4 = 0)
| 1 | 0.5 | (1/2 * 1^4 = 1/2)
| 2 | 8 | (1/2 * 2^4 = 1/2 * 16 = 8)
| 3 | 40.5 | (1/2 * 3^4 = 1/2 * 81 = 40.5)

### Summary

- For the parent function \( y = x^4 \):
- At \( x = 1 \), \( y = 1 \)
- At \( x = 2 \), \( y = 16 \)
- For the vertically compressed function \( y = \frac{1}{2} x^4 \):
- At \( x = 1 \), \( y = 0.5 \)
- At \( x = 2 \), \( y = 8 \)

Thus, we can see from the tables that for \( k = \frac{1}{2} \), the function \( y = \frac{1}{2} x^4 \) indeed results in a vertical compression of the parent function \( y = x^4 \). The \( y \) values from the compressed function are half of those from the parent function for the same \( x \) values, illustrating the effect of vertical compression.