First find the minimum point of the graph.

Since absolute value function can not be negative, the minimum point of the

graph is where .

The original function is

Set original function

                  (Add 1 to each side)

                        (Additive inverse property: )

                                (Additive identity property: )

Next make at table, fill out the table with values for .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ f(x) = |x -2|+3 \
\ x \	\  f(x) \
\ -2 \	\ 7 \
\ -1 \	\ 6 \
\ 0 \	\ 5 \
\ 1 \	\ 4 \
\ 2 \	\ 3 \

\

First, draw a co-ordinate plane.

Locate the points on co-ordinate plane and draw the graph through these points. 

Observe the graphs, both graphs have same shape and points on are 3 units higher than and 2 unit right than the points on .

The graph of  is the graph of and translated 3 units up and 2 unit right.

The graph of  is the graph of and translated 3 units up and 2 unit right. \ \