To find the transformation of a function, we need to know the basic parameters in the transformation, namely, a, h and k.
For a transformation from f(x) to g(x), given by
g(x)=a*f(x-h)+k
h = horizontal translation (to the right)
k=vertical translation (upwards)
For a>0,
0<a<1 = a vertical shrink by a scale factor of a.
a=1 no vertical stretch nor shrink
1<a = vertical stretch by a scale factor of a.
a<0 implies a reflection about the x-axis PLUS the same stretch/shrink as described above replacing a by |a|.
For the given case
g(x)=-2log(x-1) where f(x)=log(x), then
g(x)=(-2) log (x-1) +0
implying that a=-2, h=1, k=0
meaning there is a reflection about the x-axis, with a vertical stretch factor of |a|=|-2|=2, a horizontal translation to the right of h=1 and a vertical translation of k=0. This are the three transformations that you can select from the given list, neglecting k=0 which means no vertical translation.
