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How do you find the domain and range f(x)=3+5times the square root of x
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\[y=3+5\sqrt{x}\]. The thing under the square root must be non negative to be defined. The thing under the square root is x. So x must be greater than or equal to zero. Therefore \[x \in [0,\infty)\] is the domain. (That basically means any number x greater than or equal to zero. )
The lowest x we can have is x = 0. When x = 0 then y = 3. So the lowest value our y can have is 3. There is no highest value our y can have so it can go to infinity. Therefore the range is any number greater than 3. which can be written as \[y \in [3,\infty)\]
The domain is \[x \in[0,\infty)\] and the range is \[y \in[3,\infty)\]
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