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How do you find domain and range for #y=sqrt(x- 2)#?

Answer 1

Avery Alexander

The domain is #x>=2# or #D(f)=[2,+oo)# and the range is

#y=sqrt(x-2)>=0=>y>=0# or #R(f)=[0,+oo)#

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Answer 2

Eva Abramson

To find the domain of ( y = \sqrt{x - 2} ), set the expression under the square root, ( x - 2 ), greater than or equal to zero and solve for ( x ). The domain is all real numbers greater than or equal to 2.

To find the range, consider the behavior of the square root function. Since the square root of a non-negative number is always non-negative, the range of ( y = \sqrt{x - 2} ) is all real numbers greater than or equal to zero.

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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.