The graph of a periodic function is shown below. Determine the amplitude.

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The graph of a periodic function is shown below. Determine the amplitude.

I think the answer is A. If i'am wrong could explain why and your reasoning to the correct answers thanks david.

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2 Answers

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$$\text{The amplitude of}\ f= \frac{1}{2}|\max f-\min f|$$

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The amplitude of a periodic function is the distance between the highest value it achieves and the lowest value it achieves, all divided by $2$. For example, $f(x)=\sin x$ achieves maximum value of $1$, minimum value of $-1$. The distance between is $2$, hence the amplitude is $1$.

In the problem given, the maximum value is $0$, the minimum value is $-4$. The distance between is $4$, hence the amplitude is $2$.

Edit: Curious, it seems there are multiple commonly used definitions of amplitude; one in which @Sami's first answer was right, and the answer is A, and one in which my above answer (and @Sami's revised answer) is right, and the answer is C.

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