Help with Piecewise function, i had a bronchitis

[ThePook]

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!

 

[HallsofIvy]

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?

 

[chaoseverlasting]

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.

 

[HallsofIvy]

Yes, of course, thank you. The 6 is too close to the 5 on a keyboard!