What is the domain and range of #y= x^2 / (x^2-16) #?

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Answer 1 · 2017-07-15T20:03:02

Domain: #(-oo,-4) uu (-4,4) uu (4,oo)#
Range: #(-oo,oo)#

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

The denominator cannot be 0, or else the equation would be undefined.

#x^2-16 !=0#
#x^2 !=16#
#x !=+-4#

#x# cannot equal #4# or #-4#, so the domain is restricted at these values. The range is not restricted; #y# can take any value.

Domain: #(-oo,-4) uu (-4,4) uu (4,oo)#
Range: #(-oo,oo)#

We can check this by graphing the equation:

graph{x^2/(x^2-16) [-14.24, 14.24, -7.12, 7.12]}