Question 212802
Using a general form of {{{y = tan(B(x-D)) + C}}} where B = (the natural period of tan)/(period of this function), D is the phase shift and C is the vertical shift, we want an equation where {{{B = (pi)/((3*pi)/8) = 8/3}}}, {{{D = -(pi/5)}}} and C = -2. We want an equation that looks like:
{{{y = tan((8/3)(x - (-(pi/5)))) + (-2)}}}
or 
{{{y = tan((8/3)(x + pi/5)) - 2}}}
None of the answers look this this. But if we multiply out the argument of tan we get:
{{{y = tan((8/3)x + (8*pi)/15) - 2}}}
which matches answer "b"