Videos and lessons with examples and solutions to help High School Algebra 2 students
learn about the transformation of tangent graphs.

Tangent Transformation:

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 Tangent

Graphing the tangent function.

Tangent Graph

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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.

How to graph y = tan(q) for one or more periods.

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.

Tangent Graph

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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