Teacher2Teacher 
Q&A #6118 
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From: Loyd <loydlin@aol.com> To: Teacher2Teacher Public Discussion Date: 2002020309:10:13 Subject: Re: functions On 2002020114:20:00, heather wrote: > >Dr.Math, >Why is the domain of the function 3*x^1/2 divided by 2*x^1/6, why is >the domain all positive real number instead of all real numbers except >zero. >I would appreciate your help, thank you. > I thought your question was interesting. YOur problem: can be rewritten as: y=[3x^{1/2)]/[2x^(1/6)] If you the domain (x values) in the numerator are positive then the y values (range) are all positive real numbers. The same is true for the denominator. However, if the domain or x values are negative, the numerator and denominator are imaginary values. However, If you rewrite the equation as: y= 3/2[x^(3/61/6)= 3/2[x^(1/3) The last expression has a negative output in the range if the domain is negative. I hope someone at this site can explain why this happens. Try graphing the above on a TI83 and you get two different graphs; one is only in the first quadrant and the second is in 1st and 3rd quadrant. Maybe someone who has calculus limits fresh on their mind can explain why this happens.
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