Question

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)
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