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

Question

 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, we use the transformation \( y = kf(x) \), where \( k = 3 \). Thus, the new function will be:

\[ y = 3f(x) = 3x^3 \]

Now, let's calculate the values for \( y \) when \( x = 1 \) and \( x = 2 \):

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

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

So, we can complete the table as follows:

| x | y = kf(x) = 3x³ | |---|------------------| | 0 | 0 | | 1 | 3 | | 2 | 24 |

The completed table is:

| x | y = kf(x) = 3x³ | |---|------------------| | 0 | 0 | | 1 | 3 | | 2 | 24 |