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)