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

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Homework Help Overview

The discussion revolves around expressing the function (x+3)*|x-2| as a piecewise defined function, focusing on the implications of the absolute value in the context of the expression.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of the absolute value in the function, questioning how to approach the piecewise definition. There is a suggestion to graph the function alongside a non-absolute version to observe differences.

Discussion Status

Some participants have provided guidance on considering different cases based on the value of x in relation to 2. The discussion is ongoing with various interpretations being explored.

Contextual Notes

There is an emphasis on the relevance of the absolute value around (x-2) while noting that (x+3) does not have an absolute value, which may affect how the piecewise function is defined.

Bostonpancake0
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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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