Graphing transformations of trigonometric functions

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  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=2sinπ4(x+3)+1y = 2\sin \frac{\pi }{4}(x + 3) + 1
    2. y=3sec(π2xπ)1y = 3\sec (\frac{\pi }{2}x - \pi ) - 1
    3. y=2sin(4x+4π)3y = - 2\sin (4x + 4\pi ) - 3
  2. For the trigonometric function: y=tan(  x3π6  )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.
    Topic Notes
    After learning all the graphs of basic trigonometric functions, in this lesson, we are going to go a little bit further on how the graphs will be transformed as the functions change. The general form for the equation of trig functions is y = f [B(x + c)] + D, where f refers the trig function; A refers to the amplitude/steepness; B represents the period of the graph; C refers to phase shift (left or right) and D represents vertical shift (up or down). We will learn how to graph the trig function for multiple periods; state the vertical displacement, phase shift, period and amplitude; and also find the domain and range of the transformed functions.