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

       (Subtract 2.5  from each side)

                     (Additive inverse property: )

                              (Additive identity property: )

Next make at table, fill out the table with values for x > - 2.5 and  x < - 2.5.

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

\ f(x) = |x + 2.5| \
\ x \	\  f(x) \
\ -5 \	\ 2.5 \
\ -3 \	\ 0.5 \
\ 0 \	\ 2.5 \
\ 3 \	\ 5.5 \
\ 5 \	\ 8.5 \

\

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 2.5 units left than the points on .

The graph of  is the graph of and translated 2.5 units left.

 The graph of  is the graph of and translated 2.5 units left.