The region between the graph of $y = f (x)$ and the $x$-axis, shaded in this figure, has an area of 10 square units. What is the area between the graph of $y = \dfrac 12 f (-x)$ and the $x$-axis?
f(-x)/2 compared to f(x) is compacting f(x) by a factor of 2, and the f(-x) is flipping it across the y axis. However if we are trying to find the area between the figure to the x axis, flipping across the y axis is irrelevant, thus all we care about is how it got compacted. If the original area was 10 units, and we smushed it by a factor of 2, then the base would remain constant but the height would be half of it. Idk what the figure looks like, but the answer is probably 10/2 = 5.