Graphing transformations of trigonometric functions

Lessons

1. For each trigonometric function:
   (i) Graph the trigonometric function for one period.
   (ii) State the vertical displacement, phase shift, period, and amplitude.
   (iii) State the domain and the range.
   1. $y = 2\sin \frac{\pi }{4}(x + 3) + 1$
   2. $y = 3\sec (\frac{\pi }{2}x - \pi ) - 1$
   3. $y = - 2\sin (4x + 4\pi ) - 3$
2. For the trigonometric function: $y = - \tan \left( {\;\frac{x}{3} - \frac{\pi }{6}\;} \right)$
   i) Graph the trigonometric function for two periods.
   ii) State the domain and the range.