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Explain how the graph of y = -tan(4x) + 1 is related to the graph of the basic trigonometric function y = tanx

User Alexsandra
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1 Answer

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Answer: The transformed graph is reflected over the x-axis, horizontally stretched by a factor of 1/4, shifted up 1 unit, and has a period of π/4.

Explanation:

The general form of a tan graph is: y = A tan (Bx - C) + D where

  • |A| is the amplitude (vertical stretch) - irrelevant for tan graphs
  • -A is a reflection over the x-axis
  • |B| is the horizontal stretch
  • -B is a reflection over the y-axis
  • C is a horizontal shift (left or right)
  • D is a vertical shift (up or down)

  • Period is
    (\pi)/(B)
  • Phase Shift is
    (C)/(B)

In the given transformed graph of y = - tan (4x) + 1

  • A = -1 --> reflected over x-axis
  • B = 4 --> horizontally stretched by a factor of
    (1)/(4)
  • D = 1 --> shifted UP 1 unit
  • Period is
    (\pi)/(4)
User Yumee
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