To vertically stretch the parent function \( f(x) = x^3 \) by a factor of 3, we use the modified function given by:
\[ g(x) = 3f(x) = 3x^3 \]
Now, we will calculate \( g(x) \) for the provided values of \( x \):
-
For \( x = 0 \): \[ g(0) = 3(0^3) = 3 \cdot 0 = 0 \]
-
For \( x = 1 \): \[ g(1) = 3(1^3) = 3 \cdot 1 = 3 \]
-
For \( x = 2 \): \[ g(2) = 3(2^3) = 3 \cdot 8 = 24 \]
So, the completed table is:
\[ \begin{array}{|c|c|} \hline x & g(x) \ \hline 0 & 0 \ 1 & 3 \ 2 & 24 \ \hline \end{array} \]
Thus, we have \( f(x) = 0, 3, 24 \) for \( x = 0, 1, 2 \) respectively.