Question

Complete this table to vertically stretch the parent function f(x)=x^3 by a factor of 3
x y =kf(x)= ___ x^3
0 0
1 ___
2 ____

Answer 1

To vertically stretch the parent function \( f(x) = x^3 \) by a factor of 3, you would multiply the output of the parent function by 3. This means the new function will be \( y = kf(x) = 3x^3 \).

Now, we can complete the table with the given values:

1. For \( x = 0 \):
\[
y = 3(0^3) = 3 \times 0 = 0
\]

2. For \( x = 1 \):
\[
y = 3(1^3) = 3 \times 1 = 3
\]

3. For \( x = 2 \):
\[
y = 3(2^3) = 3 \times 8 = 24
\]

Now we can complete the table:

\[
\begin{array}{|c|c|}
\hline
x & y = 3f(x) = 3x^3 \\
\hline
0 & 0 \\
1 & 3 \\
2 & 24 \\
\hline
\end{array}
\]

Therefore, the completed table is:

| x | y = 3f(x) = 3x^3 |
|---|--------------------|
| 0 | 0 |
| 1 | 3 |
| 2 | 24 |