Question 335529
The square root function requires non-negative arguments.
{{{x(x-8)>=0}}}
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Break up the number line into 3 regions.
Region 1:({{{-infinity}}},{{{0}}})
Region 2:({{{0}}},{{{8}}})
Region 3:({{{8}}},{{{infinity}}})
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Choose a point in each region, not an endpoint, and calculate the product. 
If the value is not negative, that region is part of the domain.
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Region 1: {{{x=-1}}}
{{{(-1)(-1-8)>=0}}}
{{{-1(-9)>=0}}}
{{{9>=0}}}
True, this region is part of the domain.
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Region 2: {{{x=1}}}
{{{(1)(1-8)>=0}}}
{{{-7>=0}}}}
False, this region is not part of the domain.
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Region 3:{{{x=9}}}
{{{(9)(9-8)>=0}}}
{{{9>=0}}}
True, this region is part of the domain.
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The domain is then ({{{-infinity}}},{{{0}}}) U ({{{8}}},{{{infinity}}})
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{{{graph(300,300,-5,15,-10,10,sqrt(x*(x-8)))}}}