How Do You Determine the Period of a Graph with Unequal Maximums and Minimums?

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Determining the period of a graph with unequal maximums and minimums can be challenging without graphing software. The period of a periodic function is defined as the distance over which the function repeats itself. To find the period visually, one can analyze the distance between consecutive peaks or troughs on the graph. Repositioning the graph to align its center with the x-axis may help in visualizing the periodicity, but it's not strictly necessary. Understanding the definition of the period is crucial for accurately determining it from the graph.
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Homework Statement



So my book has a bunch of examples of graphs similar to sine or cosine graphs, where the maximums and minimums are the same (for example, the maximums might be 1, and the minimums will be -1). If I only have a graph to work with, I will just look at the waves and determine the period from that. But how do I determine the period of a graph that has unequal maximum and minimums? For example, all the maximums may be 7, but all the minimums will be 2. How do I determine the period of a graph like this, if I only have the graph to work with? Do I just move the graph so that its center is at the x axis? Is there anyway to determine the period of a graph like this without using graphing software to reposition the graph to the x axis? If I have to redraw it it could be difficult.

Homework Equations


The Attempt at a Solution

Thanks
 
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priceofcarrot said:

Homework Statement



So my book has a bunch of examples of graphs similar to sine or cosine graphs, where the maximums and minimums are the same (for example, the maximums might be 1, and the minimums will be -1).

If I only have a graph to work with, I will just look at the waves and determine the period from that. But how do I determine the period of a graph that has unequal maximum and minimums? For example, all the maximums may be 7, but all the minimums will be 2. How do I determine the period of a graph like this, if I only have the graph to work with? Do I just move the graph so that its center is at the x axis? Is there anyway to determine the period of a graph like this without using graphing software to reposition the graph to the x axis? If I have to redraw it it could be difficult.
...

Thanks

What is the definition of the period of a periodic function?
 


Oh god that's embarrassing.. Lol

Sorry, I just checked my work today and can't believe that I asked this question.

Thanks
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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