Question

Complete the table to vertically stretch the parent function f (x) = x3 by a
factor of 3.

x = 0, 1, 2
f(x) = 0, ?, ?

Answer 1

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 \( x \):

1. For \( x = 0 \):
\[
g(0) = 3(0^3) = 3 \cdot 0 = 0
\]

2. For \( x = 1 \):
\[
g(1) = 3(1^3) = 3 \cdot 1 = 3
\]

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.