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

Answer 1

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)#

Therefore, the domain will consist of all numbers (otherwise the solution is imaginary) where the terms under the radical are not negative.

#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)#

This is the graph:

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

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Answer 2

Genesis Allen

Domain: All real numbers x such that x ≥ -3. Range: All real numbers y such that y ≥ 0.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.