Identify the factor k for the vertical compression from the original function y=|x+6|

In the context of vertical dilations or compressions of functions, the factor \( k \) represents how the function has been changed compared to the original function.

The original function is \( y = |x + 6| \). The dilated function is given as \( y = \frac{1}{2} |x + 6| \).

To identify the factor \( k \) for the vertical compression, we compare the two functions:

• The original function has a coefficient of \( 1 \) in front of \( |x + 6| \) (which can be considered as \( k = 1 \)).
• The dilated function has a coefficient of \( \frac{1}{2} \) in front of \( |x + 6| \).

Since the coefficient is less than \( 1 \), it indicates a vertical compression. The factor \( k \) is simply the coefficient in front of the absolute value in the dilated function.

Thus, we have: \[ k = \frac{1}{2} \]

So the answer is: \[ \boxed{\frac{1}{2}} \]