g(x) is a vertical dilation of scale factor 1/4 followed by a reflection over the x-axis of f(x).
How are the graphs related?
Here we have the transformation:
g(x) = (-1/4)*f(x)
We can decompose this transformation into two ones, first, we can dilate it vertically with a factor of 1/4 (so it is a compression actually) to get:
g(x) = (1/4)*f(x)
Then we apply a reflection over the x-axis, then we will get:
g(x) = (-1/4)*f(x)
These are the relations.