Question

Complete the table to vertically stretch the parent function f(x)=x3 by a factor of 3.(2 points) x y=kf(x)= x3 0 0 1 2

Answer 1

To vertically stretch the parent function \( f(x) = x^3 \) by a factor of 3, you can use the transformation \( kf(x) = 3f(x) = 3x^3 \).

Now, we can calculate the values of \( y \) for the given \( x \) values.

1. **For \( x = 0 \)**:
\[
f(0) = 0^3 = 0
\]
\[
y = 3f(0) = 3 \cdot 0 = 0
\]

2. **For \( x = 1 \)**:
\[
f(1) = 1^3 = 1
\]
\[
y = 3f(1) = 3 \cdot 1 = 3
\]

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

Now, we can complete the table based on the above calculations:

| \( x \) | \( y = kf(x) = 3x^3 \) |
|:---------:|:--------------------------:|
| 0 | 0 |
| 1 | 3 |
| 2 | 24 |

So the completed values are:
- When \( x = 0 \), \( y = 0 \)
- When \( x = 1 \), \( y = 3 \)
- When \( x = 2 \), \( y = 24 \)