Understanding Transformations of the Tangent Function

The video tutorial explains how to transform and graph the function y = 2 * tan(3x + π/2) + 1. It covers the vertical stretch by a factor of two, calculates the period as π/3 radians, determines the phase shift as left π/6 radians, and explains the vertical shift up one unit. The tutorial then guides viewers through graphing the transformed tangent function, including handling vertical asymptotes and replicating the graph for additional periods.

What is the effect of the coefficient 'a' in the function y = 2 * tan(3x + π/2) + 1?

• It shifts the graph to the right.

• It stretches the graph vertically.

• It compresses the graph horizontally.

• It reflects the graph over the x-axis.

How is the period of the function y = 2 * tan(3x + π/2) + 1 calculated?

• By subtracting π from the coefficient of x.

• By adding π to the coefficient of x.

• By multiplying π by the coefficient of x.

• By dividing π by the coefficient of x.

What is the phase shift of the function y = 2 * tan(3x + π/2) + 1?

• π/3 radians to the right

• π/6 radians to the left

• π/3 radians to the left

• π/6 radians to the right

What is the vertical shift of the function y = 2 * tan(3x + π/2) + 1?

• Up by two units

• Down by two units

• Up by one unit

• Down by one unit

What is the period of the basic tangent function?

• π/2 radians

• π radians

• 3π radians

• 2π radians

Where are the vertical asymptotes located for the function y = 2 * tan(3x + π/2) + 1?

• At x = π/3 and x = 0

• At x = -π/6 and x = π/6

• At x = π/6 and x = -π/6

• At x = -π/3 and x = 0

How does the vertical stretch affect the graph of the tangent function?

• It shifts the graph upwards.

• It makes the graph wider.

• It shifts the graph downwards.

• It makes the graph narrower.

What is the new horizontal axis for the function y = 2 * tan(3x + π/2) + 1?

• y = 2

• y = 1

• y = -1

• y = 0

How do you extend the graph of the tangent function?

• By decreasing the period.

• By increasing the period.

• By copying and pasting the initial segment.

• By adding more vertical asymptotes.

What is the total period covered when extending the graph by one more segment?

• 2π/3 radians

• 3π/2 radians

• π radians

• π/3 radians