Given-that-f-x-x-for-0-x-lt-2-0-for-2-x-3-is-periodic-with-period-3-units-find-the-value-of-f-5-and-f-5-sketch-the-graph-of-f-x-for-x-between-3-and-6-please-i-really-need-

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Question Number 66116 by Rio Michael last updated on 09/Aug/19

$$Giventhatf\left(x\right)=\{\begin{array}{l}x,for0⩽x<2\\ 0,for2⩽x⩽3\end{array}$$$$isperiodicwithperiod3units,$$$$findthevalueoff\left(5\right)andf(-5)$$$$sketchthegraphoff\left(x\right)forxbetween-3and6$$$$$$$$pleaseireallyneedexplanationswhensolvingthefirstpartofthequestion$$$$thanks$$

Commented by Prithwish sen last updated on 09/Aug/19

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}(\mathrm{x}+3)=\mathrm{f}(\mathrm{x}-3)\because \mathrm{f}\mathrm{is}\mathrm{a}\mathrm{periodic}\mathrm{with}3\mathrm{unit}$$$$\because \mathrm{f}\left(5\right)=\mathrm{f}\left(8\right)\mathrm{or}\mathrm{f}\left(2\right)=0$$$$\mathrm{and}\mathrm{f}(-5)=\mathrm{f}(-2)\mathrm{or}\mathrm{f}(-8)=\mathrm{x}=-5$$

Commented by Rio Michael last updated on 09/Aug/19

$$thankyou$$

Commented by Rio Michael last updated on 09/Aug/19

$$butidontthefactthat$$$$f(x+3)=f(x-3)why?$$$$andyoursolving$$

Commented by Prithwish sen last updated on 09/Aug/19

$$\because \mathrm{it}\mathrm{is}\mathrm{a}\mathrm{periodic}\mathrm{funtion}\mathrm{of}3\mathrm{unit}\mathrm{it}\mathrm{will}\mathrm{repeat}\mathrm{itself}$$$$\mathrm{after}\mathrm{or}\mathrm{before}\mathrm{every}3\mathrm{unit}.$$$$\mathrm{that}\mathrm{is}\mathrm{why}\mathrm{f}(\mathrm{x}-3),\mathrm{f}\left(\mathrm{x}\right),\mathrm{f}(\mathrm{x}+3)\mathrm{will}\mathrm{have}\mathrm{the}$$$$\mathrm{same}\mathrm{value}.$$

Commented by Rio Michael last updated on 09/Aug/19

$$thankyousir$$

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