Answer: B) The graph of f(x) is horizontally stretched.
Step-by-step explanation: We are given an absolute function [tex]f(x)=-\frac{2}{3} |x+4|-6[/tex].
The standard equation of an absolute function is [tex]f(x)= a|x-h|+k[/tex].
Where (h,k) is the vertex of the absolute function.
If we compare [tex]f(x)=-\frac{2}{3} |x+4|-6[/tex] and [tex]f(x)= a|x-h|+k[/tex], we can see a=[tex]-\frac{2}{3}[/tex], h= -4 and h= -6.
Therefore, vertex of the given function is (-4,-6).
Because we have value of a is a negative number so it would open down.
An absolute function always have domain " All real numbers".
Therefore, first, third and fourth options are incorrect.
So, the second option would only be applicable.
B) The graph of f(x) is horizontally stretched.
