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Papessa [141]
3 years ago
5

What are the period and phase shift for f(x) = −4 tan(x − π)?

Mathematics
2 answers:
MrRissso [65]3 years ago
4 0
The general form for the tangent equation is y = (a)tan(bx-c)+d where a is the amplitude, b is the period and c is the phase shift.  The period of the tangent graph is pi, and the formula to solve for the period is then period= \frac{ \pi }{b}.  Our b value is 1, so the period of this tangent curve is pi.  The formula for the phase shift is p.s.= \frac{c}{b} and for us that is pi/1.  So the period for this curve is pi, and the phase shift is pi units to the right.
nadya68 [22]3 years ago
3 0
\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
% function transformations for trigonometric functions
% templates
f(x)=Asin(Bx+C)+D
\\\\
f(x)=Acos(Bx+C)+D\\\\
f(x)=Atan(Bx+C)+D
\\\\
-------------------

\bf \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}

\bf ~~~~~~\textit{reflection over the y-axis}
\\\\
\bullet \textit{ horizontal shift by }\frac{C}{B}\\
~~~~~~if\ \frac{C}{B}\textit{ is negative, to the right}\\\\
~~~~~~if\ \frac{C}{B}\textit{ is positive, to the left}\\\\
\bullet \textit{vertical shift by }D\\
~~~~~~if\ D\textit{ is negative, downwards}\\\\
~~~~~~if\ D\textit{ is positive, upwards}

\bf \bullet \textit{function period or frequency}\\
~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\
~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)

with that template in mind, let's see this one.

\bf f(x)=\stackrel{A}{-4}tan(\stackrel{B}{1}x\stackrel{C}{-\pi })+\stackrel{D}{0}
\\\\\\
\stackrel{period}{\cfrac{2\pi }{B}\implies \cfrac{2\pi }{1}\implies 2\pi }
\\\\\\
\stackrel{phase/horizontal~shift}{\cfrac{C}{B}\implies \cfrac{-\pi }{1}}\implies -\pi \qquad \textit{shifted to the right by }\pi \textit{ units}
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