a)First find the minimum point of the graph.

Since absolute value function can not be negative, the minimum point of the

graph is where .

b) The function and  

The original function is

Set original function

              (Subtract 3 from each side)

                    (Additive inverse property: )

                            (Additive identity property: ) \ \

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

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

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

\

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 3 units higher than the points on .

The graph of  is the graph of and translated 3 units up.

c)The function and \ \

The original function is

Set original function

                   (Divide each side by 2)

                           (Cancel common terms)

                              (Divide: )

                  (Add 1 to each side)

                        (Additive inverse property: )

                                   (Additive identity property: ) 

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

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

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

\

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 2 units right side than the points on .

The graph of  is the graph of and translated 3 units right.

d)The function and \ \

The original function is

Set original function

            (Subtract 3 from each side)

              (Additive inverse property: )

                       (Additive identity property: )

The original function is

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

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

\ f(x) = |2(x-1)| \
\ x \	\  f(x) \
\ -2 \	\ 6 \
\ -1 \	\ 4 \
\ 0 \	\ 2 \
\ 1 \	\ 0 \
\ 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 3 units higher than and 2 units rihgt side the points on .

The graph of  \ \ is the graph of and translated 3 units up and 2 units rihgt.

 The graph of  \ \ is the graph of and translated 3 units up and 2 units rihgt.