Answer:
g(x) = -|8x| +5
Step-by-step explanation:
We assume that "compress ... by a factor of 1/2" means that horizontal distances on the graph of f(x) are to be reduced to 1/2 their value to obtain the graph of g(x). (We prefer to call this "scaled by 1/2", so that we avoid the ambiguity associated with using a fractional value as a compression factor.)
If k is the horizontal scale factor, then the horizontal scaling makes ...
g(x) = f(x/k)
Reflection across the x-axis changes the sign of function values, so our compressed, reflected function is ...
g(x) = -f(x/(1/2)) = -f(2x)
g(x) = -(|4(2x)| -5)
g(x) = -|8x| +5
