To determine which table shows that \( y = kf(x) \) results in the parent function \( y = |x + 4| \) being vertically stretched by a factor of \( k = 3 \), we need to first identify the values of the parent function \( y = |x + 4| \) for the given \( x \) values and then multiply those values by \( 3 \).
Let's first calculate \( f(x) = |x + 4| \) for the specified \( x \) values:
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For \( x = 0 \): \[ f(0) = |0 + 4| = |4| = 4 \] \( kf(0) = 3 \times 4 = 12 \)
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For \( x = 1 \): \[ f(1) = |1 + 4| = |5| = 5 \] \( kf(1) = 3 \times 5 = 15 \)
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For \( x = 2 \): \[ f(2) = |2 + 4| = |6| = 6 \] \( kf(2) = 3 \times 6 = 18 \)
Thus, the resulting values for \( y = kf(x) \) for \( x = 0, 1, 2 \) are \( 12, 15, 18 \), respectively.
Now, let's examine the provided responses to find a match:
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Response 1: \[ \begin{align*} x & \quad y = kf(x) \ 0 & \quad 12 \ 1 & \quad 15 \ 2 & \quad 18 \ \end{align*} \] This matches what we calculated.
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Response 2: \[ \begin{align*} x & \quad y = kf(x) \ 0 & \quad -12 \ 1 & \quad -15 \ 2 & \quad -18 \ \end{align*} \] This does not match.
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Response 3: \[ \begin{align*} x & \quad y = kf(x) \ 0 & \quad -12 \ 1 & \quad -15 \ 2 & \quad -18 \ \end{align*} \] This is identical to Response 2, so it does not match.
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Response 4: \[ \begin{align*} x & \quad y = kf(x) \ 0 & \quad 1.3 \ 1 & \quad 1.7 \ 2 & \quad 2 \ \end{align*} \] This does not match.
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Response 5: \[ \begin{align*} x & \quad y = kf(x) \ 0 & \quad 4 \ 1 & \quad 5 \ 2 & \quad 6 \ \end{align*} \] This shows the original function values before the vertical stretch.
Therefore, the correct answer is Response 1: \[ \begin{align*} x & \quad y = kf(x) \ 0 & \quad 12 \ 1 & \quad 15 \ 2 & \quad 18 \ \end{align*} \]