Write the equation for the transformation of f(x) = |x| as shown in the graph.

y = 2|x-3| + 1

Step-by-step explanation:

The vertex of g(x) = |x| is at (0,0)

We have moved the vertex to ( 3,1)

y = f(x) + C  C > 0 moves it up

y = |x| + 1 for the shift up 1

y = f(x + C)  C < 0 moves it right

y = |x-3|  for the shift to the right 3

y = Cf(x)  C > 1 stretches it in the y-direction

y = 2|x| since  it is stretched by a factor of 2 in the y direction

Combining

y =2|x-3| + 1