What is the vertex of the function f (x) = |x-9,|+2

The vertex is thus (9, 2).

Step-by-step explanation:

The vertex of y = |x| is at (0, 0). Appending "+2" to this function shifts the vertex up by 2 units. Replacing x in |x| with x - 9 translates the whole graph to the right 9 units. The vertex is thus (9, 2).