Question 795636
{{{ f(x) = sqrt( x*( 16 - x^2 ) ) }}}
If {{{ x = 0 }}}, the function exists- it is {{{ 0 }}}
If {{{ x = 4 }}} or
if {{{ x = -4 }}}, {{{ f(x) = 0 }}} also
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If {{{ x > 4 }}},  {{{ f(x) }}} is the square root
of a negative number, so the function
does not exist if {{{ x >4 }}}
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If {{{ x < -4 }}} then {{{ sqrt( x*( 16 - x^2 ) ) }}} is
the square root of a negative times a negative,
so the function exists
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If {{{ -4 < x < 0 }}}, f(x) does not exist because you
have the square root of a negative times a positive
which is a negative
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If  {{{ 0 < x < 4 }}}, f(x) exists because you have 
the square root of a positive times a positive
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Putting this together, the domain is:
{{{ x < = -4 }}}
{{{ 0 < = x <= 4 }}}
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Here's the plot:
 {{{ graph( 400, 400, -6, 6, -8, 8, sqrt( x*( 16 - x^2 ))  ) }}}