Identify the Transformations and Asymptotes of Tangent Graph

The video tutorial covers the tangent function, focusing on its properties, graph characteristics, and the unit circle. It explains the concept of asymptotes and the period of the tangent function, highlighting that the period is π, not 2π. The tutorial also discusses the effects of vertical stretching and horizontal compression on the graph, emphasizing the importance of understanding these concepts for solving problems related to tangent and cotangent functions.

What is the tangent of an angle defined as in terms of coordinates?

• x^2 + y^2

• y^2 - x^2

• x/y

• y/x

Where are the asymptotes located on the tangent graph?

• At 2π and 4π

• At π and 2π

• At 0 and π

• At π/2 and 3π/2

What is the period of the tangent function?

• π

• 2π

• π/2

• 3π

How does a factor of 3 affect the tangent graph?

• It shifts the graph to the right

• It compresses the graph horizontally

• It compresses the graph vertically

• It stretches the graph vertically

What is the effect of a horizontal stretch on the tangent graph?

• It shifts the graph upwards

• It increases the period

• It decreases the period

• It increases the amplitude

How far should the asymptotes be moved to achieve a period of 2π?

• π/2

• π/4

• π

• 2π

What is the general formula for the location of asymptotes in the tangent function?

• X = 2πn

• X = nπ/2

• X = πn

• X = π/2 + nπ