How do you find the domain and range for $y= (x+3)^0.5$ ?

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Answer 1 · 2018-05-29T17:06:55

Domain: ${x|x>=-3}$ or $[-3, oo)$

Range: ${y|y>=0}$ or $[0, oo)$

$y= (x+3)^0.5$

$y= (x+3)^(1/2)$

$y= sqrt(x+3)$

So the domain will be all numbers where the terms under the radical are not negative (otherwise the solution is imaginary).

$x+3>=0$

$x>=-3$

Domain: ${x|x>=-3}$ or $[-3, oo)$

Now the range at $x=-3; y=0$ but it will always be greater than or equal to 0.

Range: ${y|y>=0}$ or $[0, oo)$

Here is the graph:

graph{sqrt(x+3) [-6, 14, -1.28, 8.72]}

How do you find the domain and range for y= (x+3)^0.5y= (x+3)^0.5?