\[\left( \mathbf{i} \right)~f\text{ }\left( x \right)\text{ }=\text{ }2\text{ }(sin\text{ }x),\text{ }0\text{ }\le \text{ }(x)\text{ }\le \text{ }\pi \]

Since, \[g\text{ }\left( x \right)\text{ }=\text{ }sin\text{ }x\]is a periodic function with period\[\pi \].

Therefore, \[f\text{ }\left( x \right)\text{ }=\text{ }2\text{ }sin\text{ }x\] is a periodic function with period \[\pi .\]

Hence, we draw the graph of \[f\text{ }\left( x \right)\text{ }=\text{ }2\text{ }sin\text{ }x\]in the interval \[\left[ 0,\text{ }\pi  \right].\]

The values of \[f\text{ }\left( x \right)\text{ }=\text{ }2\text{ }sin\text{ }x\]at various points in \[\left[ 0,\text{ }\pi  \right]\]are listed in below:

The curve is:

\[\left( \mathbf{ii} \right)~g\text{ }\left( x \right)\text{ }=\text{ }3\text{ }sin\text{ }\left( x\text{ }-\text{ }\pi /4 \right),\text{ }0\text{ }\le \text{ }x\text{ }\le \text{ }5\pi /4\]

Since, if \[f\text{ }\left( x \right)\]is a periodic function with period \[~T\], then \[f\text{ }\left( ax\text{ }+\text{ }b \right)\]is periodic with period \[T/\left| a \right|.\]

Therefore\[,\text{ }g\text{ }\left( x \right)\text{ }=\text{ }3\text{ }sin\text{ }\left( x\text{ }-\text{ }\pi /4 \right)\] is a periodic function with period \[\pi .\]

Hence, we draw the graph of\[g\text{ }\left( x \right)\text{ }=\text{ }3\text{ }sin\text{ }\left( x\text{ }-\text{ }\pi /4 \right)\] in the interval \[\left[ 0,\text{ }5\pi /4 \right]\]. The values of\[g\text{ }\left( x \right)\text{ }=\text{ }3\text{ }sin\text{ }\left( x\text{ }-\text{ }\pi /4 \right)\] at various points in \[\left[ 0,\text{ }5\pi /4 \right]\] are listed below:

The curve is: