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

              (Subtract 7 from each side)

                    (Additive inverse property: )

                            (Additive identity property: )

              (Multiply each side by negative one)

                                  (Product of two same signs is positive)

The original function is

Set original function

                (Add 3 to each side)

                      (Additive inverse property: )

                                  (Additive identity property: )

Next make at table, fill out the table with values for x > 3 and  x < 3,.

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

\   \ f(x) = |x - 3| \	\   \ f(x) = -|x|+7 \
\ x \	\  f(x) \	\   \ X \   \	\   \ f(x) \
\ -4 \	\ 7 \	\ -2 \	\ 7 \
\ -2 \	\ 5 \	\ -1 \	\ 6 \
\ 0 \	\ 3 \	\ 0 \	\ 5 \
\ 2 \	\ 1 \	\ 1 \	\ 4 \
\ 4 \	\ 1 \	\ 2 \	\ 3 \

\

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 different shapes and points on and

have common point is .

The graphs of  and have in common point is .