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.
Step-by-step 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 [tex]\dfrac{\pi}{B}[/tex]
- Phase Shift is [tex]\dfrac{C}{B}[/tex]
In the given transformed graph of y = - tan (4x) + 1
- A = -1 --> reflected over x-axis
- B = 4 --> horizontally stretched by a factor of [tex]\dfrac{1}{4}[/tex]
- D = 1 --> shifted UP 1 unit
- Period is [tex]\dfrac{\pi}{4}[/tex]
