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 of the given tables 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 evaluate the parent function \( f(x) = |x + 4| \) at the given values of \( x \), and then multiply those results by 3.

1. Compute \( f(x) = |x + 4| \):

- For \( x = 0 \):
\( f(0) = |0 + 4| = 4 \)

- For \( x = 1 \):
\( f(1) = |1 + 4| = 5 \)

- For \( x = 2 \):
\( f(2) = |2 + 4| = 6 \)

2. Multiply by \( k = 3 \):

- For \( x = 0 \):
\( y = 3f(0) = 3 \cdot 4 = 12 \)

- For \( x = 1 \):
\( y = 3f(1) = 3 \cdot 5 = 15 \)

- For \( x = 2 \):
\( y = 3f(2) = 3 \cdot 6 = 18 \)

The resulting values of \( y = kf(x) \) are:

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

Now, we can compare these results to the provided tables.

The correct table that represents these results is:

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

Thus, the correct response is the table that shows:

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