When graphing a tangent transformation, start by using a theta and tan(theta) t-table for -pi/2 to pi/2. In the case of y = Atan(Bx) or y = Atan(B(x - h)), define Bx or B(x-h) to be equal to theta and solve for x. Now use this equation to create a x and Atan(Bx) or Atan(B(x - h)) table, which will give coordinate pairs to plot.
This video provides an example of graphing a transformation of the basic tangent function when the period has changed.
Transforming the Tangent Graph
How to graph y = tan(q) for one or more periods.
Intercepts and Asymptotes of Tangent Functions:
The tangent identity is tan(theta) = sin(theta)/cos(theta), which means that whenever sin(theta) = 0, tan(theta) = 0, and whenever cos(theta) = 0, tan(theta) is undefined (dividing by zero). When the tangent function is zero, it crosses the x-axis. Therefore, to find the intercepts, find when sin(theta) = 0. To find the vertical asymptotes determine when cos(theta) = 0.
How to find the x-intercepts and vertical asymptotes of the graph of y = tan(x).
Graphing the tangent function.
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