To determine which of the given tables represents the function \( y = kf(x) \) where \( f(x) = |x + 4| \) is vertically stretched by a factor of \( k = 3 \), we start by identifying how this transformation changes the parent function.
The parent function is: \[ f(x) = |x + 4| \]
When we apply a vertical stretch by a factor of 3, we have: \[ y = kf(x) = 3|x + 4| \]
Next, we calculate the values of \( 3|x + 4| \) for the given \( x \) values from the tables:
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For \( x = 0 \): \[ f(0) = |0 + 4| = 4 \] \[ y = 3f(0) = 3 \times 4 = 12 \]
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For \( x = 1 \): \[ f(1) = |1 + 4| = 5 \] \[ y = 3f(1) = 3 \times 5 = 15 \]
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For \( x = 2 \): \[ f(2) = |2 + 4| = 6 \] \[ y = 3f(2) = 3 \times 6 = 18 \]
From these calculations, we see that the values for \( y = kf(x) \) when \( k = 3 \) and applying the parent function \( f(x) = |x + 4| \) are:
- For \( x = 0 \), \( y = 12 \)
- For \( x = 1 \), \( y = 15 \)
- For \( x = 2 \), \( y = 18 \)
Therefore, the correct response is the fourth table:
| x | y = kf(x) | |---|-----------| | 0 | 12 | | 1 | 15 | | 2 | 18 |