SOLUTION: Please solve and show steps thank you! y=|6x|?

Question 19261: Please solve and show steps thank you! y=|6x|?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
y=|6x|..in these absolute value questions ,we have to split the problem in to 2 cases
case1...the variable under absolute value sign is +ve..in this case it means 6x is +ve or x is +ve..then since 6x is +ve we will have y=|6x|=+6x........(1)
case2...the variable under absolute value sign is -ve..in this case it means 6x is -ve or x is -ve..then since 6x is -ve we will have y=|6x|=-6x........(2)
so we have to solve these 2 cases seperately to get 2 solutions..each case can however be dealt with in the normal manner.this is the general theory for solution of these eqns.
now coming to domain...that is the value x can take for a legal /meaningful equation connecting y....here we find there is no problem and x can take any real value...
now coming to range..that is the value y will take for the above values of x...we find from analysis above that whether x is +ve or -ve y is always +ve..
so range of y is all positive real numbers.

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