SOLUTION: Find the domain and range of {{{y=4+sqrt(x-2)}}}

Question 128482: Find the domain and range of

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

Remember you cannot take the square root of a negative value. So that means the argument must be greater than or equal to zero (i.e. the argument must be positive)

Set the inner expression greater than or equal to zero

Add 2 to both sides

Combine like terms on the right side

So that means x must be greater than or equal to in order for x to be in the domain

So the domain in set-builder notation is

So here is the domain in interval notation: [2,

)

Now the endpoint of the domain corresponds to the endpoint of the range. So simply plug in into

Start with the given function

Plug in

Subtract

Take the square root of zero to get zero

Add

So when ,

This means that the minimum of the range is which tells us that the range is

So the range in set-builder notation is

and the range in interval notation is

[4,

)

Now if we graph , we can visually verify our answer.

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