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 7 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 + 4|-7 \
\ x \	\  f(x) \
\ -4 \	\ -7 \
\ -2 \	\ -9 \
\ 0 \	\ -11 \
\ 2 \	\ -13 \
\ 4 \	\ -15 \

\

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 7 units lower than and 4 units left the points on .

The graph of  is the graph of and translated 7 units down and 4 units left.

\ \