Which of the following tables shows that y=kf(x)

Question

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 table represents the function \( y = kf(x) \) with a stretch factor \( k = 3 \) for the parent function \( y = |x + 4| \), we first need to calculate the values of \( f(x) = |x + 4| \) for the given \( x \) values, and then find the corresponding values for \( y = kf(x) \).

For the parent function \( f(x) = |x + 4| \):

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

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

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

Thus, the values for \( y = kf(x) \) with \( k = 3 \) are:

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

Now, looking at the provided options:

The correct table is:

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

This shows that \( y = kf(x) \) results in the parent function \( y = |x + 4| \) being vertically stretched by a factor of \( k = 3 \).