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]}

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