Me ! how is the graph of mc027-1.jpg related to its parent function, mc027-2.jpg?

We will try to approach it generally. If we have a function y=f(x) and we have then y=f(2x), then the graph of the function will be horizontally compressed. If we take f(x/2), the graph of the function will be dilated. (To get horizontal shifts, we need f(x+a), which is not the case here; for example is horizontally shifted relative to its parent function). If we consider -y=f(x), then the graph of this new function is the graph of the parent function flipped along the x-axis. If we consider y=f(-x) (which is the case here, since ) we have that the graph of the new function is the same as the old graph, just flipped along the y-axis. Each of those transformations is independent; combining our observations we see that the last answer is the correct one.