Pls help, sorry for the trouble

Question

Link to image of problem 

Answer 1

The generical equation for transformed tangent functions is:

y = Atan(B(x - C)) + D

Where A is the vertical stretch, B is calculated from Period = π/B, C is the horizontal shift, and D is the vertical shift.

The normal period for y = tan(x) is π but in this case, the period is π/4 (π/8 one direction from zero and another π/8 the other direction from zero makes π/4). So π/4 = π/B or B = 4. That makes the generic equation:

y = Atan(4(x - C)) + D

There is no vertical or horizontal shift so that makes the equation:

y = Atan(4x)

Normally, the y = tan(x) contain the point (π/4, 1) or, beginning at zero, and moving right by 1/4 period, the y-value should be 1. In this case, beginning at zero and going 1/4 period (so π/16), we see the y-value is 2. That means A = 2.

Final equation: y = 2tan(4x)