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Question Number 141937 by cesarL last updated on 24/May/21

Write and graph the equation of the graph of y=sin(πx)  It is stretched up by a factor of 5 and shifted (1/2) unit to the right  Help me please

$${Write}\:{and}\:{graph}\:{the}\:{equation}\:{of}\:{the}\:{graph}\:{of}\:{y}={sin}\left(\pi{x}\right) \\ $$$${It}\:{is}\:{stretched}\:{up}\:{by}\:{a}\:{factor}\:{of}\:\mathrm{5}\:{and}\:{shifted}\:\frac{\mathrm{1}}{\mathrm{2}}\:{unit}\:{to}\:{the}\:{right} \\ $$$${Help}\:{me}\:{please} \\ $$$$ \\ $$

Commented by MJS_new last updated on 25/May/21

y=f(x)  shift d to the left y=f(x+d)  shift d to the right y=f(x−d)  shift d up y=f(x)+d  shift d down y=f(x)−d  stretch by d horizontally y=d×f(x)  stretch by d vertically y=f((x/d))  “stretch up” seems to mean stretch vertically  ⇒  y=5sin (π(x−(1/2)))

$${y}={f}\left({x}\right) \\ $$$$\mathrm{shift}\:{d}\:\mathrm{to}\:\mathrm{the}\:\mathrm{left}\:{y}={f}\left({x}+{d}\right) \\ $$$$\mathrm{shift}\:{d}\:\mathrm{to}\:\mathrm{the}\:\mathrm{right}\:{y}={f}\left({x}−{d}\right) \\ $$$$\mathrm{shift}\:{d}\:\mathrm{up}\:{y}={f}\left({x}\right)+{d} \\ $$$$\mathrm{shift}\:{d}\:\mathrm{down}\:{y}={f}\left({x}\right)−{d} \\ $$$$\mathrm{stretch}\:\mathrm{by}\:{d}\:\mathrm{horizontally}\:{y}={d}×{f}\left({x}\right) \\ $$$$\mathrm{stretch}\:\mathrm{by}\:{d}\:\mathrm{vertically}\:{y}={f}\left(\frac{{x}}{{d}}\right) \\ $$$$``\mathrm{stretch}\:\mathrm{up}''\:\mathrm{seems}\:\mathrm{to}\:\mathrm{mean}\:\mathrm{stretch}\:\mathrm{vertically} \\ $$$$\Rightarrow \\ $$$${y}=\mathrm{5sin}\:\left(\pi\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)\right) \\ $$

Commented by cesarL last updated on 25/May/21

thnks sir

$${thnks}\:{sir} \\ $$

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