How do I find the range of these functions without using a graph $y=-2+sqrt(16-x^2)$ ?

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Answer 1 · 2018-06-09T06:45:50

$-2<=-2+sqrt(16-x^2)<=2$

Since $sqrt(16-x^2)>=0$ we get
$-2<=-2+sqrt(16-x^2)$
Since $-x^2<=0$ we get

$sqrt(16-x^2)<=4$
or
$-2+sqrt(16-x^2)<=2$

How do I find the range of these functions without using a graph y=-2+sqrt(16-x^2)y=-2+sqrt(16-x^2)?