What effect does replacing x with x + 2 have on the graph for the function f (x) ?

f (x) = |x-3|+2

The graph is shifted 2 units left.

The graph is shifted 2 units down.

The graph is shifted 2 units right.

The graph is shifted 2 units up.

Step-by-step explanation:

The vertex of f (x) = |x-3|+2 is at (3, 2).

Replacing x with x+2 results in g (x) = f (x) = | (x+2) - 3|+2, or

g (x) = f (x) = |x+2-3|+2, or

g (x) = f (x) = |x - 1|+2 The vertex of this graph is at (1, 2).

The effect of replacing x with x + 2 is a horizontal shift to the left, of 2 units, of the original graph.