Mathematics, 03.07.2019 18:00 bananaslada
What are the amplitude, period, phase shift, and midline of f(x) = 2 sin(x + π) − 4?
Answers: 1
![\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ % templates f(x)=Asin(Bx+C)+D \\\\ f(x)=Acos(Bx+C)+D\\\\ f(x)=Atan(Bx+C)+D \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis}](/tpl/images/0047/2644/eeb83.png)
![\bf f(x)=2sin(x+\pi )-4\implies f(x)=\stackrel{A}{2}sin(\stackrel{B}{1}x\stackrel{C}{+\pi })\stackrel{D}{-4} \\\\[-0.35em] ~\dotfill\\\\ \textit{Amplitude}\implies 2 \\\\\\ \stackrel{phase}{\textit{Horizontal Shift}}\implies \cfrac{C}{B}\implies \cfrac{+\pi }{1}\implies +\pi \impliedby \pi \textit{ units to the left} \\\\\\ \textit{Period}\implies \cfrac{2\pi }{B}\implies \cfrac{2\pi }{1}\implies 2\pi \\\\\\ \textit{Vertical Shift}\implies D\implies -4\impliedby \textit{4 units downwards}](/tpl/images/0047/2644/787dc.png)
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What are the amplitude, period, phase shift, and midline of f(x) = 2 sin(x + π) − 4?...
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