Given the transformation ), i know f(x) flips over the y-axis, but how does it horizontally translate?

there is no horizontal translation. a transformation including a horizontal translation would have looked like    there is a reflection in the y-axis and a horizontal expansion.the horizontal expansion factor is the reciprocal of that coefficient inside of the function. the reciprocal of 0.5 is      so there is a horizontal expansion by a factor of 2.======in general,    if  (the reciprocal of b) is greater than 1, then it is a horizontal expansion by a factor of  .if  is between 0 and 1, then it is a horizontal compression by a factor of .if  is negative, then there is a reflection in the y-axis.keep in mind that translations (shifts left/right and up/down) are always last before compressions, expansions, and reflections.