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Question Number 84121 by Rio Michael last updated on 09/Mar/20

$$\mathrm{given}\mathrm{that}$$$$\mathrm{g}\left(x\right)=\{\begin{array}{l}x+2,\mathrm{if}0⩽x<2\\ x^2,\mathrm{if}2⩽x<4\end{array}$$$$\mathrm{is}\mathrm{periodic}\mathrm{of}\mathrm{period}4.$$$$\mathrm{sketch}\mathrm{the}\mathrm{curve}\mathrm{for}\mathrm{g}\left(x\right)\mathrm{in}\mathrm{the}\mathrm{interval}$$$$0⩽x<8$$$$\mathrm{evaluate}\mathrm{g}(-6).$$

Commented by MJS last updated on 09/Mar/20

$$\mathrm{period}4\Rightarrow g\left(x\right)=g(x+4z);z\in \mathbb{Z}$$$$\Rightarrow g(-6)=g(-6+4\times 2)=g\left(2\right)=2^2=4$$

Commented by Rio Michael last updated on 09/Mar/20

$$\mathrm{thanks}\mathrm{sir}\mathrm{how}\mathrm{about}\mathrm{the}\mathrm{graph}$$

Commented by MJS last updated on 09/Mar/20

$$\mathrm{the}\mathrm{graph}\mathrm{in}[0;4[\mathrm{is}\mathrm{the}\mathrm{same}\mathrm{as}\mathrm{in}[4;8[$$$$xg\left(x\right)$$$$02$$$$.52.5$$$$13$$$$1.53.5$$$$24$$$$2.56.25$$$$39$$$$3.512.25$$$$416\mathrm{is}\mathrm{not}\mathrm{part}\mathrm{of}g\left(x\right)\mathrm{but}\mathrm{the}\underset{x\to 4^{-}}{\lim }g\left(x\right)$$$$\Rightarrow \mathrm{the}\mathrm{graph}\mathrm{seems}\mathrm{to}\mathrm{reach}\mathrm{it}\mathrm{but}\mathrm{it}{\mathrm{doesn}}^{\prime }\mathrm{t}$$$$\mathrm{mark}\mathrm{the}\mathrm{point}(4\mid 16)\mathrm{with}\mathrm{a}‘‘{\circ }^{″}$$$$42$$$$4.52.5$$$$...$$$$816\mathrm{same}\mathrm{as}(4\mid 16)$$

Commented by Rio Michael last updated on 10/Mar/20

$$\mathrm{thanks}\mathrm{sir}$$

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