Okay I understand, this isn't a formulaic question because we don't have the function definitions to figure out each absolute value, so we have to use intuition and a graphical interpretation of the average value so we can pick an answer.
Here's my thought process;
A. hmm, a trig graph with a 'mean value' of 2, isn't mean the same as average? well yeah it is, but this isn't an unrestricted trig graph so while a single cycle of this graph (and indeed any trig graph with no domain restriction) would have avg = 2, we have 1.5 cycles which shifts the average up a fair bit. Not this one!
B. one way to think of the average value is that 'flattening out stones' thing and it looks like, if we set the surface of these stones to be at y=2, we'll have too many stones to nicely fit in the two little gaps under 2 that this graph has. It's not rigorous, but we can suspect that this one isn't the answer.
C. This one's tempting, we can figure out the area using two triangles and remembering that the part below the axis needs to be subtracted and see if it works;
and by our formula, width * average value = area
it looks like avg = 2, C is the answer
let's look at the last 2 anyway,
D. simple triangle, area = 24 so avg value = 4
E. not so simple, it looks like this one works because the triangle has an area of 8 and a width of 4, but if you notice, this graph extends all the way to x=0 with a height of 0 so its actual width is 6 and avg = area/width = 8/6 not 2
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