Can we identify the right sketch of a transformed function?

Can we identify the right sketch of a transformed function?

Question

The diagram below shows the graph of the function $y = f(x)$.

The graph of the function $y = -f(x+1)$ is drawn in which of the following diagrams?

Solution

The graph $y = f(x+1)$ is a translation of the original graph by one unit to the left.

This is followed by a reflection in the $x$-axis to get $y = -f(x+1)$, and so the answer is (a).

(Doing the reflection followed by the translation gives the same answer.)