Question

how the transformations of the functions f(x)=15tanx and g(x)=tanx+15 differ?

Answer 1

g(x)=tanx+15 effects the y so y intersept is + 15 not 0
  f(x)==(15 sin(x))/cos(x)

Answer 2

The transformation of f(x)=15tanx would be achieved by dilating y=tanx graph 15 times. This transformation will cause y'=15 y. This will increase the value of dilation become 15 times of the original

The transformation of g(x)=15tanx would be achieved by shifting y=tanx graph 15 right. This transformation will cause x'=x+15. This will change the value from tan x into tan(x+15)