For each of the functions below, determine the amplitude, period, phase shift, vertical translation, domain and range. Then sketch or cycle of the function with clear labelling of both $$ x $$ and $$ y $$-axis. a) $$ y=-\frac{3}{2} \sin \left[4\left(x-\frac{\pi}{6}\right)\right]-5 $$

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Valdez Watkins · Accepted Answer

Amplitude: $$ \frac{3}{2} $$, Period: $$ \frac{\pi}{2} $$, Phase Shift: $$ \frac{\pi}{6} $$ to the right, Vertical Translation: down 5 units, Domain: all real numbers, Range: $$[- \frac{13}{2}, - \frac{7}{2}]$$

For each of the functions below, determine the amplitude, period, phase shift, vertical translation, domain and range. Then sketch or cycle of the function with clear labelling of both \( x \) and \( y \)-axis. a) \( y=-\frac{3}{2} \sin \left[4\left(x-\frac{\pi}{6}\right)\right]-5 \)

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For each of the functions below, determine the amplitude, period, phase shift, vertical translation, domain and range. Then sketch or cycle of the function with clear labelling of both \( x \) and \( y \)-axis. a) \( y=-\frac{3}{2} \sin \left[4\left(x-\frac{\pi}{6}\right)\right]-5 \)

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