Which of the following tables shows that y=kf(x) results in the parent function y=|x+4| being vertically stretched by a k factor of 3?(1 point)

Question

Responses

x y=kf(x)
0 4
1 5
2 6
x y equals k f left parenthesis x right parenthesis 0 4 1 5 2 6

x y=kf(x)
0 −12
1 −15
2 −18
x y equals k f left parenthesis x right parenthesis 0 negative 12 1 negative 15 2 negative 18

x y=kf(x)
0 12
1 15
2 18
x y equals k f left parenthesis x right parenthesis 0 12 1 15 2 18

x y=kf(x)
0 1.3
1 1.7
2 2
x y equals k f left parenthesis x right parenthesis 0 1.3 1 1.7 2 2
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Answer 1

To determine which table shows the vertical stretch of the parent function \( y = |x + 4| \) by a factor of \( k = 3 \), we first need to find the points on the parent function and then apply the vertical stretch.

The parent function \( y = |x + 4| \) at various points:

• At \( x = 0 \): \( y = |0 + 4| = 4 \)
• At \( x = 1 \): \( y = |1 + 4| = 5 \)
• At \( x = 2 \): \( y = |2 + 4| = 6 \)

Now, applying the vertical stretch by a factor of \( k = 3 \):

• For \( x = 0 \): \( y = 3 \cdot 4 = 12 \)
• For \( x = 1 \): \( y = 3 \cdot 5 = 15 \)
• For \( x = 2 \): \( y = 3 \cdot 6 = 18 \)

Now let's look at the provided responses for \( y = kf(x) \):

1. Table 1:

   • \( (0, 4) \)
   • \( (1, 5) \)
   • \( (2, 6) \)
   • Incorrect (these values are not the result of a vertical stretch)

2. Table 2:

   • \( (0, -12) \)
   • \( (1, -15) \)
   • \( (2, -18) \)
   • Incorrect (values are negative)

3. Table 3:

   • \( (0, 12) \)
   • \( (1, 15) \)
   • \( (2, 18) \)
   • Correct (these values match the expected results of stretching by a factor of 3)

4. Table 4:

   • \( (0, 1.3) \)
   • \( (1, 1.7) \)
   • \( (2, 2) \)
   • Incorrect (values are much lower than expected)

Thus, the correct table showing that \( y = kf(x) \) results in the parent function \( y = |x + 4| \) being vertically stretched by a factor of \( k = 3 \) is Table 3.