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 9 to each side)

                   (Additive inverse property: )

                            (Additive identity property: )

Next make at table, fill out the table with values for x > 9 and  x < 9.

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

\ f(x) = |x| + 9 \
\ x \	\  f(x) \
\ – 6 \	\ 15 \
\ – 3 \	\ 12 \
\ 0 \	\ 9 \
\ 3 \	\ 12 \
\ 6 \	\ 15 \

\

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 9 units higher than the points on .

The graph of  is the graph of and translated 9 units up.

The graph of  is the graph of and translated 9 units up.