What are the steps to change an absolute value equation to a piecewise function? What part of the equation affects the domain restrictions?

Question

anonymous · Answer

Well. Do you understand what an absolute value equation is? DO you know what a piecewise function is?

myininaya · Answer

|x|=  x if x>0
       -x if x<0
        0 if x=0

anonymous · Answer

yes i know both

myininaya · Answer

so if we have |x-2|
then we would write
|x-2|=   x-2 if x-2>0
          -(x-2) if x-2<0
              0   if x-2=0

anonymous · Answer

i just need steps

myininaya · Answer

do you got it?

myininaya · Answer

all you must do is use the definition i gave you above

anonymous · Answer

the original? so you just follow that? and what part of the equation affects the domain restrictions?

myininaya · Answer

domain is all real numbers for |x|
unless you have a fraction or square root or even root or trig functions(some trig functions don't exist everywhere)

myininaya · Answer

and that list might have some others that may make a function not continuous everywhere

anonymous · Answer

so abs value affects the domain restrictions?

myininaya · Answer

no | | doesn't affect the domain restrictions

anonymous · Answer

does the amplitude affect it?