SOLUTION: Find the domain and range of the given function. Explain your answers. H(h)= 2h + 3 sqrt h + 10 So far I have figured out that the domain is: All real numbers h greater than

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Question 963677: Find the domain and range of the given function. Explain your answers.
H(h)= 2h + 3 sqrt h + 10
So far I have figured out that the domain is: All real numbers h greater than or equal to 0. And the range is: All real numbers H(h)=10. If these are incorrect, what did I do wrong, and what should they be?
I need an explanation for both the domain and range. I do not understand how to verbally explain why the domain and range are what they are.
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
Domain: Because the square root function, which is one of the components of the function, requires a non-negative argument so this forces the domain to be non-negative.
Range: Each of the individual functions that make up the entire function are positive function and the entire function is the sum of the three functions. The minimum of occurs at as does the minimum of . Both these values are so the only term that contributes to the value is the constant term . So the minimum of the function is and the maximum if unbounded making the range [,).