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Draw the graph of f(x) = {{:(x-2n,""2n ...

Draw the graph of ` f(x) = {{:(x-2n,""2n le xlt 2n +1), "" (1/2,""2n+1 le x lt 2n+2):}`
periodic? If yes, what is its period?

Text Solution

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`f(x) = {{:(x-2n," "2n le x lt 2n + 1),(1/2," "2n+1 le xlt 2n+2):}`
`{{:(...),(...),(x+2"," - 2 le x lt -1),(1/2","-1lexlt0),(x","0 le xlt 1),(1/2"," 1le xlt 2),(x-2"," 2 le x lt 3),(1/2", "3le xlt 4),(x-4"," 4 le xlt 5),(...),(...):}`
Graph of the function is as follows:

Clearly, the function is periodic with period 2.
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