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

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-axisC is a horizontal shift (left or right)D is a vertical shift (up or down)Period is Phase Shift is

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

A = -1  -->  reflected over x-axisB = 4  --> horizontally stretched by a factor of D = 1  -->  shifted UP 1 unitPeriod is