Tangent Function Properties and Graphs

The video tutorial explains how to analyze and graph the function y = 3tan(2x - 4π). It covers finding the period, identifying asymptotes, and understanding the effects of phase shifts. The tutorial also demonstrates how to graph the function, highlighting the changes in steepness and intercepts due to the coefficient and phase shift.

What is the period of the function y = 3tan(2x - 4π)?

• π/2

• 2π

• π/4

• π

In a basic tangent graph, where are the asymptotes located?

• π/4 and -π/4

• π and -π

• π/2 and -π/2

• 0 and π

How does the period of a tangent function affect the distance between asymptotes?

• It triples the distance

• It doubles the distance

• It halves the distance

• It does not affect the distance

What is the phase shift of the function y = 3tan(2x - 4π)?

• π/4

• 2π

• π

• π/2

After a phase shift, where does the asymptote originally at π/4 move to?

• 5π/4

• 7π/4

• 9π/4

• 11π/4

How far apart are the asymptotes in the adjusted graph of y = 3tan(2x - 4π)?

• 2π

• π/4

• π/2

• π

What effect does the coefficient 3 have on the graph of y = 3tan(2x - 4π)?

• It changes the period

• It increases the steepness

• It shifts the graph vertically

• It changes the phase shift

What is the complete distance between the asymptotes after adjusting for the new period?

• 2π

• π/2

• π/4

• π

How does the graph of y = 3tan(2x - 4π) compare to a basic tangent graph?

• It is more steep

• It is inverted

• It is less steep

• It has the same steepness

What pattern does the graph of y = 3tan(2x - 4π) repeat between the asymptotes?

• Tangent

• Sinusoidal

• Parabolic

• Linear