SOLUTION: y = x^2 / (x2-16) I could use some help finding the domain and range. Any help would be greatly appreciated!!

Question 383534: y = x^2 / (x2-16)
I could use some help finding the domain and range. Any help would be greatly appreciated!!
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!

Domain : possible value for x. If x=+4 or -4, there is a division by zero, all other value are possible, hence Dom(y(x))=R-{+4,-4}
Range : all values that y reaches, seek for the inverse :

y*x^2-16y = x^2
x^2(1-y)=-16y

x^2=16y/(y-1)

thus 1 is not allowed for y, more over y/(y-1) has to be positive :

cases : y>0 and y-1>0<=>y>1,

y<0 and y-1<0<=>y<1, hence y<0

so the range of y is : Range(y(x))=]-oo;0]U[1,+oo[
Graph :

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