How to Write (x+3)*|x-2| as a Piecewise Function?

[Bostonpancake0]

Write (x+3)*(absolute value of (x-2)) as a peice-wise defined function.

How do I set about doing this, considering (x+3) is not an absolute value??

 

[eumyang]

Try graphing both
y = (x + 3)|x - 2|
and
y = (x + 3)(x - 2) (without the absolute value)
by hand or by using a graphing utility. You will notice something when you compare the graphs.

 

[Bostonpancake0]

ahhhh thank you

 

[HallsofIvy]

The fact that there is no absolute value around x+ 3 is irrelevant. There is an absolute value or x- 2 so look at x< 2, x> 2.