Question 893780
Not sure if you mean,
{{{f(x)=-(1/3)abs(x-4)}}}
of 
{{{f(x)=-1/(3*abs(x-4))}}}
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We'll do it both ways. 
First, {{{f(x)=-(1/3)abs(x-4)}}}
Absolute value function always returns a positive value so f(x) will always be negative. It equals zero at {{{x=4}}}
So the domain is all values of x, ({{{-infinity}}},{{{infinity}}}).
The range is all values less than or equal to zero, ({{{-infinity}}},{{{0}}}].
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{{{graph(300,300,-10,10,-10,10,-(1/3)*abs(x-4))}}}
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Next, {{{f(x)=-1/(3*abs(x-4))}}}
Again, values will be negative but in this case the values approach zero but never equal zero. 
Domain is all points except {{{x=4}}} since division by zero is undefined. 
So the domain is ({{{-infinity}}},{{{4}}})U({{{4}}},{{{infinity}}}).
The range is all values less than zero, ({{{-infinity}}},{{{0}}}).
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{{{graph(300,300,-5,5,-5,5,-1/(3*abs(x-4)))}}}