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 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
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

Answer 1

To determine which of the given tables represents the function \( y = kf(x) \) where \( f(x) = |x + 4| \) is vertically stretched by a factor of \( k = 3 \), we start by identifying how this transformation changes the parent function.

The parent function is:
\[ f(x) = |x + 4| \]

When we apply a vertical stretch by a factor of 3, we have:
\[ y = kf(x) = 3|x + 4| \]

Next, we calculate the values of \( 3|x + 4| \) for the given \( x \) values from the tables:

1. **For \( x = 0 \)**:
\[ f(0) = |0 + 4| = 4 \]
\[ y = 3f(0) = 3 \times 4 = 12 \]

2. **For \( x = 1 \)**:
\[ f(1) = |1 + 4| = 5 \]
\[ y = 3f(1) = 3 \times 5 = 15 \]

3. **For \( x = 2 \)**:
\[ f(2) = |2 + 4| = 6 \]
\[ y = 3f(2) = 3 \times 6 = 18 \]

From these calculations, we see that the values for \( y = kf(x) \) when \( k = 3 \) and applying the parent function \( f(x) = |x + 4| \) are:

- For \( x = 0 \), \( y = 12 \)
- For \( x = 1 \), \( y = 15 \)
- For \( x = 2 \), \( y = 18 \)

Therefore, the correct response is the fourth table:

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