Question

Complete the table to show that y=kf(x) results in the parent function being vertically compressed when k=12 . Write your answer as a whole number or decimal x y=kf(x)= x4 0 1 2

Answer 1

To show that \( y = kf(x) \) results in the parent function being vertically compressed when \( k = \frac{1}{12} \), we need to decide on a parent function \( f(x) = x^4 \).

For any \( k < 1 \), the function will be vertically compressed compared to the parent function.

Let's calculate the values of \( y = \frac{1}{12} f(x) = \frac{1}{12} x^4 \) for the given values of \( x = 0, 1, 2 \).

1. **For \( x = 0 \)**:
- \( f(0) = 0^4 = 0 \)
- \( y = \frac{1}{12} f(0) = \frac{1}{12} \cdot 0 = 0 \)

2. **For \( x = 1 \)**:
- \( f(1) = 1^4 = 1 \)
- \( y = \frac{1}{12} f(1) = \frac{1}{12} \cdot 1 = \frac{1}{12} \approx 0.0833 \)

3. **For \( x = 2 \)**:
- \( f(2) = 2^4 = 16 \)
- \( y = \frac{1}{12} f(2) = \frac{1}{12} \cdot 16 = \frac{16}{12} \approx 1.3333 \)

Now we can complete the table:

| \( x \) | \( y = kf(x) \) | \( kf(x) = \frac{1}{12} x^4 \) |
|---------|------------------|--------------------------------|
| 0 | 0 | 0 |
| 1 | 0.0833 | 0.0833 |
| 2 | 1.3333 | 1.3333 |

To summarize:
- When \( k = \frac{1}{12} \), the parent function \( y = x^4 \) is vertically compressed, and the resulting values yield \( y \approx 0, 0.0833, 1.3333 \) for \( x = 0, 1, 2 \) respectively.