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 −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 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 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

x y=kf(x)
0 12
1 15
2 18

Answer 1

To determine which table represents the function \( y = kf(x) \) where \( f(x) = |x + 4| \) vertically stretched by a factor of \( k = 3 \), we first need to understand how vertical stretching works.

The parent function \( f(x) = |x + 4| \) has specific output values for certain inputs:

• For \( x = 0 \): \[ f(0) = |0 + 4| = 4 \]

• For \( x = 1 \): \[ f(1) = |1 + 4| = 5 \]

• For \( x = 2 \): \[ f(2) = |2 + 4| = 6 \]

When we stretch the parent function by a factor of 3, we multiply the outputs by 3:

• For \( x = 0 \): \[ kf(0) = 3 \cdot 4 = 12 \]

• For \( x = 1 \): \[ kf(1) = 3 \cdot 5 = 15 \]

• For \( x = 2 \): \[ kf(2) = 3 \cdot 6 = 18 \]

Now, we look for a table that corresponds with the calculated values for \( kf(x) \):

• First Response:

  • \( (0, -12) \)
  • \( (1, -15) \)
  • \( (2, -18) \)
  • Does not match.

• Second Response:

  • \( (0, 4) \)
  • \( (1, 5) \)
  • \( (2, 6) \)
  • This is just the parent function, does not match.

• Third Response:

  • \( (0, 1.3) \)
  • \( (1, 1.7) \)
  • \( (2, 2) \)
  • Does not match.

• Fourth Response:

  • \( (0, 12) \)
  • \( (1, 15) \)
  • \( (2, 18) \)
  • This matches with our calculations.

Thus, the correct table showing \( y = kf(x) \) resulting in the parent function being vertically stretched by a factor of \( k = 3 \) is:

x y = kf(x)

• 0 12
• 1 15
• 2 18