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.