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 12 1 15 2 18

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 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 4
1 5
2 6

Answer 1

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 first need to look at the values of \( f(x) = |x + 4| \) for the relevant \( x \) values and then see how they would look after applying the vertical stretch.

1. Calculate \( f(x) = |x + 4| \) for the given \( x \) values:
- For \( x = 0 \): \( f(0) = |0 + 4| = |4| = 4 \)
- For \( x = 1 \): \( f(1) = |1 + 4| = |5| = 5 \)
- For \( x = 2 \): \( f(2) = |2 + 4| = |6| = 6 \)

2. Now, we apply the vertical stretch by a factor of \( k = 3 \):
- For \( x = 0 \): \( y = 3f(0) = 3 \times 4 = 12 \)
- For \( x = 1 \): \( y = 3f(1) = 3 \times 5 = 15 \)
- For \( x = 2 \): \( y = 3f(2) = 3 \times 6 = 18 \)

Thus, the resulting values for \( y = kf(x) \) would be:
- For \( x = 0 \): \( y = 12 \)
- For \( x = 1 \): \( y = 15 \)
- For \( x = 2 \): \( y = 18 \)

Looking at the response options, the correct table that matches these values is:

**Response:**
```
x y = kf(x)
0 12
1 15
2 18
```

So, the correct answer is the first option.