Question

Complete the table to vertically stretch the parent function f of x equals X cubed by a factor of 3 0 1 2

Answer 1

To vertically stretch the parent function \( f(x) = x^3 \) by a factor of 3, we modify the function as follows:

\[
g(x) = 3 \cdot f(x) = 3x^3
\]

Now, let's compute the values for different inputs (0, 1, and 2) for both the parent function \( f(x) \) and the vertically stretched function \( g(x) \).

### Table

| \( x \) | \( f(x) = x^3 \) | \( g(x) = 3x^3 \) |
|---------|------------------|---------------------|
| 0 | 0 | 0 |
| 1 | 1 | 3 |
| 2 | 8 | 24 |

### Explanation:
- For \( x = 0 \):
- \( f(0) = 0^3 = 0 \)
- \( g(0) = 3 \cdot 0^3 = 0 \)

- For \( x = 1 \):
- \( f(1) = 1^3 = 1 \)
- \( g(1) = 3 \cdot 1^3 = 3 \)

- For \( x = 2 \):
- \( f(2) = 2^3 = 8 \)
- \( g(2) = 3 \cdot 2^3 = 24 \)

This gives you the completed table for the parent function and the vertically stretched function.