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

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-axisC 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) + 1A = -1  -->  reflected over x-axisB = 4  --> horizontally stretched by a factor of [tex]\dfrac{1}{4}[/tex]D = 1  -->  shifted UP 1 unitPeriod is [tex]\dfrac{\pi}{4}[/tex]