Question

How is the graph of g (x) = - __1 4 f (x) related to the graph of f ?

Answer 1

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.