Answer:
B, f(x) = 2|x - 2| + 6
Step-by-step explanation:
the functions shown have vertical stretches, horizontal shifts, and vertical shifts as a transformation
we do not need to focus on the stretch, and moreso the shifts
the horizontal shift takes place on the x-axis and it is written with the parent function (in this case the parent function is |x|). when the shift is negative (ex: x -2), this means that the x-coordinate would be positive. if the shift is positive (ex: x + 2) the x-coordinate would be negative
the vertical shift takes place on the y-axis and unlike the horizontal shift, is written on the outside of the parent function, like the +6 and -6 in each of the functions we are given. when a shift is positive (ex: +6), the y-coordinate is positive and when a shift is negative (ex: -6) the y coordinate is negative
using this information, we can see that 2|x - 2| + 6 fits this criteria, as we have a positive vertex
therefore the answer is B, f(x) = 2|x - 2| + 6
