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

WhichWitchIsWhich
Nov 13, 2017

#1**+2 **

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

Melody
Nov 15, 2017