Help with Piecewise function, i had a bronchitis

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Homework Help Overview

The original poster presents a problem involving the evaluation of an absolute value function expressed as a piecewise function. Additionally, there is a mention of expressing the area of a rectangle with a given perimeter, where one side is defined as length x.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants discuss the definition of piecewise functions and the conditions under which the absolute value function can be expressed in piecewise form. Questions are raised about the specific intervals for the function |x+5| and the corresponding expressions for those intervals.

Discussion Status

The discussion is ongoing, with participants providing clarifications regarding the conditions for the absolute value function. There is an acknowledgment of a typographical error in the original post, but no consensus has been reached on the overall approach to the problem.

Contextual Notes

The original poster mentions being unwell, which may have impacted their ability to engage with the material. The problems presented are part of a larger set assigned for an upcoming quiz.

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Homework Statement


I had a bronchitis the past week, and I have no idea what to do with this problem, my teacher gave us two problems out of 28 from the upcoming quiz, and this is one of the two.

What the following absolute value using a piecewise function?
y=|x+5|+2


Express the area of a rectangle with a perimeter of 100 with 1 size as length is x.



Any help would be appreciate!
 
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Presumably you textbook defines "piecewise". That is a function that is defined by a specific formula on one interval and then another formula on second formula.

Also you should know that |x|= x if x>= 0 and |x|= -x if x< 0. In particular, |x+5|= x+ 5 if x+6>=0 and |x+5|= -(x+5) if x< 0.

Okay, for what values of x is x+5>=0? What is |x+5|+ 2 there? For what values of x is x+5> 0? What is |x+5|+ 2 there?
 
HallsofIvy said:
Also you should know that |x|= x if x>= 0 and |x|= -x if x< 0. In particular, |x+5|= x+ 5 if x+6>=0 and |x+5|= -(x+5) if x< 0.

Dont you mean |x+5|=x+5 if x+5>=0 and |x+5|=-(x+5) if x<-5.
 
Yes, of course, thank you. The 6 is too close to the 5 on a keyboard!
 

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