Question 215432
y=x^2/(x^2-16) state the domain and range 
I figured out the domain (I think):
x^2-16=0
(x-4)(x+4)=0
x=-4 or x=+4 
The domain is "all x not equal to -4 or 4". Is that correct? 
And I can't find the range, can anybody help?
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The domain is correct.
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Range?
Notice that the horizontal asymptote is x^2/x^2 = 1
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So the graph would never cross the line y = 1.
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Since the numerator is larger than the denominator,
y is above y=1 for x^2>16 (i.e. x>4 or x<-4)
and y is below y=0 for x^2 < 16 (i.e. -4< x <4
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Looks like the Range is All Real Numbers except 0< y <1
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{{{graph(400,300,-10,10,-10,10,x^2/(x^2-16))}}}
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Cheers,
Stan H.