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what is the period of the function f(x) shown in the graph?

8pi

Step-by-step explanation:

A "period" of a function just means the length of one cycle. For a graph, what I usually do is pick one of the crests or troughs (high points or low points) and see how many units it takes for me to get from one crest to the next crest, or one trough to the next trough. But for any problem like this, you just need to pick a point on the curve and figure out how long it takes you to get to the same point on the next wave. Crests and troughs are just easier to follow than any random point in the middle. (Looking up a video about this would probably help you visualize it better.)

In your case, there's a trough at -2pi and another trough at 6pi, so it takes 8pi to get from one to the other. You can double check this by choosing the crest at -6pi and seeing how many units it takes for you to get from -6pi to the next crest at 2pi. Again, the answer is 8pi, so the period of this function will be 8pi.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.