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Suppose that the graph of a certain function, y=f(x), has the property that if it is shifted 20 units to the right, then the resulting graph is identical to the original graph of y=f(x).  What is the smallest positive a such that if the graph of y=f(x/5)$ is shifted a units to the right, then we know that the resulting graph is identical to the original graph of $y=f(x/5)?

 

Thanks! :DD

 Nov 13, 2017
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Suppose that the graph of a certain function, y=f(x), has the property that if it is shifted 20 units to the right, then the resulting graph is identical to the original graph of y=f(x).  What is the smallest positive a such that if the graph of y=f(x/5)$ is shifted a units to the right, then we know that the resulting graph is identical to the original graph of $y=f(x/5)?

 

The answer is 5*20=100

This is when we know for sure that the  translation of a (in the right direction) will make the graph identical.

 

Here is a simple example

https://www.desmos.com/calculator/znwt41svqb

 Nov 15, 2017

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