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

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To express (x+3)*|x-2| as a piecewise function, consider the behavior of the absolute value component, |x-2|, which changes at x=2. For x<2, |x-2| equals -(x-2), while for x≥2, |x-2| equals (x-2). Thus, the function can be defined as two separate expressions: for x<2, it simplifies to -(x+3)(x-2), and for x≥2, it simplifies to (x+3)(x-2). The absence of an absolute value around (x+3) does not affect the piecewise definition. Graphing both functions reveals distinct behaviors based on the value of x relative to 2.
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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??
 
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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.
 
ahhhh thank you
 
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.
 

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