Which of the following equations matches the function shown above?
2 answers:
Remark
Any answer that does not alter x cannot be correct. That means that A and C are both incorrect. The cycle of y = cos(x) is 2*pi in both those cases. What that means is that the cos will start at its highest point and 2*pi later will be back at its highest point.
The above paragraph explains what A and C do not do. But what is it that they do? A will give an amplitude of 1/4 which means that the highest point is y = 1/4 and the lowest point is y = -1/4. C will do the same thing except that y will = 4 and - 4 at at its highest and lowest point.
So what's the answer between B and D? Your graph shows the cycle ending at pi/2. Which graph does that? y = cos(1/4 pi) or y = cos(4pi)? The way to reason that out is to look at the end point. It is at x = 1.57. What should it be? It should be x = 2*pi or x =6.28. What do you have to do to get 1.57 to equal 6.28?
Answer you must multiply x by 4
So the answer to the question is B. Look to see that my graph is the same as yours. The red line is y = cos(1/4 x). The blue one is the one you want.
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