Answer:
g(x) = 1/2|x - 1| + 2
Explanation:
You were almost there, you just got the slope wrong.
original vertex (h, k): (0, 0)
transformed vertex (h', k'): (1, 2)
original slope: 1
transformed slope: m = (3-2)/(3-1) = 1/2 pick any 2 points to find the slope
equation for the transformed function shown in the graph:
g(x) = 1/2|x - h'| + k'
g(x) = 1/2|x - 1| + 2