SOLUTION: Hi there, how would you find the range of y=absx/x ? How do you find it without graphing it? ie. in an exam situation where you don't have much time

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Question 1117791: Hi there, how would you find the range of y=absx/x ?
How do you find it without graphing it? ie. in an exam situation where you don't have much time
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39799)   (Show Source): You can put this solution on YOUR website!


y can be or it can be .
y cannot be 0.
x cannot be 0.

RANGE: { -1, 1 }
Answer by ikleyn(53763)   (Show Source): You can put this solution on YOUR website!
.
Concretely for  f(x) = ,  this function takes only TWO values:


    if  x > 0,  then |x| = x, and therefore  f(x) =  = 1.


    if  x = 0,  then the function f(x) is NOT DEFINED.


    if  x < 0,  then |x| = -x,  hence  f(x) =  = -1.



So, the range of this function is the set of the two values  {-1,1},  while its domain is the set of all real numbers except of {0}.


To be successful at the exam,  you need

      1)  to know the basics well,  and

      2)  to have some experience in solving typical problems.


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