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 8 to each side)

            (Apply additive inverse property: )

                         (Apply additive identity property: )

Next make at table, fill out the table with values for x > 8 and  x < 8.

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

\ f(x) = | x | – 8 \
\ x \	\  f(x) \
\ – 2 \	\ – 6 \
\ –1 \	\ – 7 \
\ 0 \	\ – 8 \
\  1 \	\ – 7 \
\ 2 \	\ – 6 \

\

First, draw a co-ordinate plane.

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

Graph for the absolute value function

Observe the graphs, both graphs have same shape and

points on are 8 units lower than the points on .

The graph of  is the graph of and translated 8 units down.

The graph of  is the graph of and translated 8 units down.