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

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Question 128482: Find the domain and range of

y=4%2Bsqrt%28x-2%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=4%2Bsqrt%28x-2%29 Start with the given expression

Remember you cannot take the square root of a negative value. So that means the argument x-2 must be greater than or equal to zero (i.e. the argument must be positive)

x-2%3E=0 Set the inner expression greater than or equal to zero

x%3E=0%2B2Add 2 to both sides


x%3E=2 Combine like terms on the right side


So that means x must be greater than or equal to 2 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 x=2 of the domain corresponds to the endpoint of the range. So simply plug in x=2 into y=sqrt%28x-2%29%2B4


y=sqrt%28x-2%29%2B4 Start with the given function


y=sqrt%282-2%29%2B4 Plug in x=2


y=sqrt%280%29%2B4 Subtract


y=0%2B4 Take the square root of zero to get zero


y=4 Add


So when x=2, y=4


This means that the minimum of the range is y=4 which tells us that the range is y%3E=4


So the range in set-builder notation is



and the range in interval notation is

[4,)



Now if we graph y=sqrt%28x-2%29%2B4 , we can visually verify our answer.

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28x-2%29%2B4%29+