sign correction

F_X(x) = If[x  <  (-1) / 2, 0, If[x  <  0, 8 / 9 - (2 / 3 * 4^((-x) - 1 / 2)), If[x  <  1 / 2, 0.5555555555555556, 1 - (2 / 3 * 4^((-x)))]]]
B1: (1 / 2, F_X(1 / 2))
B0: ((-1) / 2, F_X((-1) / 2))
b = 0 (slider from -2 to 2, step 0.1)
a = 1 (slider from -3 to 3, step 0.1)
F_Y(x) = F_X((x - b) / a)
C0: (((-1) / 2 * a) + b, F_X((-1) / 2))
C1: ((1 / 2 * a) + b, F_X(1 / 2))
c = false
F_Z = If(a > 0, F_Y, 1 - F_Y(x))
D0 = If(a > 0, C0, (b - a / 2, 1))
D1 = If(a > 0, C1, (a / 2 + b, 4 / 9))
F_{aX+b} = If(c, F_Z, F_Y)
E0 = If(c, D0, C0)
E1 = If(c, D1, C1)
q_X(α) = If[0  <  α  <  2 / 9, -1 / 2, If[2 / 9 ≤ α  <  5 / 9, (-1) / 2 - log(4 / 3 - (3 * α / 2)) / log(4), If[5 / 9  <  α ≤ 2 / 3, 1 / 2, If[2 / 3  <  α  <  1, ((-log((3 / 2 * (1 - α))))) / log(4)]]]]
B = (0.5555555555555556, 0.25)
q_Y(α) = (a * q_X(α)) + b
C: (5 / 9, a / 4 + b)
q_Z = If(a > 0, q_Y, q_Y(1 - y))
D = If(a > 0, C, (4 / 9, a / 4 + b))
q_{aX+b} = If(c, q_Z, q_Y)
E = If(c, D, C)