How do you find the domain and range of $y = -sqrt(x+6)+7$ ?

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Answer 1 · 2018-06-19T05:34:32

The domain is $x in [-6,+oo]$ . The range is $y in (-oo,7]$

The function is

$y=-sqrt(x+6)+7$

What's under the square root sign must be $>=0$

Therefore,

$x+6>=0$

$=>$ , $x>=-6$

The domain is $x in [-6,+oo]$

When $x=-6$

$y=-sqrt(-6+6)+7=0+7=7$

And when $x-> +oo$

$y->(-sqrt(+oo+6)+7)=-oo$

The range is $y in (-oo,7]$

graph{-sqrt(x+6)+7 [-32.17, 71.9, -28.34, 23.65]}

How do you find the domain and range of y = -sqrt(x+6)+7 y = -sqrt(x+6)+7 ?