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)

             (Apply additive inverse property: )

                         (Apply additive identity property: )

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

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

\ 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)

               (Apply additive inverse property: )

                           (Apply additive identity property: )

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

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

\ 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 right 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 right.

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

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