Identify the factor k for the vertical compression from the original function y=|x+6| to the dilated function y=1/2|x+6|

1 answer

To identify the factor \( k \) for the vertical compression from the original function \( y = |x + 6| \) to the dilated function \( y = \frac{1}{2}|x + 6| \), we can compare the two functions.

In the context of vertical dilations, the general form of a function undergoing vertical compression can be expressed in terms of a factor \( k \):

\[ y = k f(x) \]

where \( f(x) \) is the original function. In this case, \( f(x) = |x + 6| \) and the dilated function is given as \( y = \frac{1}{2}|x + 6| \).

Here, we see that:

\[ k = \frac{1}{2} \]

Since \( k \) is less than 1, this indicates a vertical compression by a factor of \( \frac{1}{2} \) from the original function \( y = |x + 6| \) to the dilated function \( y = \frac{1}{2}|x + 6| \).

So, the factor \( k \) for the vertical compression is:

\[ \boxed{\frac{1}{2}} \]