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 4 to each side)

               (Additive inverse property: )

                           (Additive identity property: )

Next make at table, fill out the table with values for| x |> 4 and | x |<  - 4.

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

\ f(x) = |x | - 4 \
\ x \	\  f(x) \
\ -2 \	\ -2 \
\ -1 \	\ -3 \
\ 0 \	\ -4 \
\ 1 \	\ -3 \
\ 2 \	\ -2 \

\

First, draw a co-ordinate plane.

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

The original function is \ \

Set original function

        (Add 4 to each side)

               (Additive inverse property: )

                           (Additive identity property: )

Next make at table, fill out the table with values for x > 4 and x <  - 4.

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

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

\

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

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

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

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

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