To determine which table represents the function \( y = kf(x) \) with a stretch factor \( k = 3 \) for the parent function \( y = |x + 4| \), we first need to calculate the values of \( f(x) = |x + 4| \) for the given \( x \) values, and then find the corresponding values for \( y = kf(x) \).
For the parent function \( f(x) = |x + 4| \):
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For \( x = 0 \): \[ f(0) = |0 + 4| = |4| = 4 \] \[ y = 3f(0) = 3 \times 4 = 12 \]
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For \( x = 1 \): \[ f(1) = |1 + 4| = |5| = 5 \] \[ y = 3f(1) = 3 \times 5 = 15 \]
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For \( x = 2 \): \[ f(2) = |2 + 4| = |6| = 6 \] \[ y = 3f(2) = 3 \times 6 = 18 \]
Thus, the values for \( y = kf(x) \) with \( k = 3 \) are:
- For \( x = 0 \), \( y = 12 \)
- For \( x = 1 \), \( y = 15 \)
- For \( x = 2 \), \( y = 18 \)
Now, looking at the provided options:
The correct table is:
x | y = kf(x)
0 | 12
1 | 15
2 | 18
This shows that \( y = kf(x) \) results in the parent function \( y = |x + 4| \) being vertically stretched by a factor of \( k = 3 \).