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

Question

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 |