Using translation concepts, it is found that the function graphed is defined by:
D. y = |x - 2| + 3.
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function has the format of the absolute value function, y = |x|, which has vertex at (0,0). Here, the vertex is at (2,3), that is, the function was shifted:
- 2 units to the right, that is, x -> x + 2.
- 3 units up, that is, y -> y + 3.
Hence the definition is given by:
D. y = |x - 2| + 3.
More can be learned about translation concepts at