# Graphing transformations of trigonometric functions

##### Examples

###### Lessons

- 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. - 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.

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###### 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.###### Basic Concepts

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