Question
Identify the factor k for the vertical compression from the original function y=|x+6| to the dilated function y=1/2|x+6|
Answers
GPT-4o mini
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:
\[
\boxed{\frac{1}{2}}
\]
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:
\[
\boxed{\frac{1}{2}}
\]