Question #8a32e

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Answer 1 · 2017-05-17T12:14:39

Domain : $x <= -3 or x >= 0 or (-oo,3] uu [0,oo)$
Range : # y >=0

$y=sqrt(x^2+3x)$ , Domain: under root must be #>=0 or

$x (x+3) >= 0$ critical points are $x=0 , x= -3$

when $x <= -3$ ; $x (x+3) >= 0$ and

when $x >= 0$ ; $x (x+3) >= 0$ and

when $-3 < x < 0$ ; $x (x+3) <= 0$

So Domain : $x <= -3 or x >= 0 or (-oo,3] uu [0,oo)$

Range : $y >=0 or [0,oo)$ graph{(x^2+3x)^0.5 [-40, 40, -20, 20]} [Ans]