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 3 to each side)

                  (Additive inverse property: )

                               (Additive identity property: )

                    (Multiply each side by negative one)

                              (Product of two same signs is positive)

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

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

\ f(x) = -|x| - 3 \
\ x \	\  f(x) \
\ -2 \	\ -5 \
\ -1 \	\ -4 \
\ 0 \	\ -3 \
\ 1 \	\ -4 \
\ 2 \	\ -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 3 units lower than the points on .

The graph of  is the graph of and translated 3 units down.

 The graph of  is the graph of and translated 3 units down.