Question

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

Answer 1

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)`