# How do you find the domain and range of #f(x) =sqrt(x-2)#?

Domain

Range

sqrt(x-2 [-10, 10, -5, 5]}) graph

Just sketch out the intended use.

The typical root function is:

Regarding range, the function we were given does not have a K value; instead, the range extends from 0 to infinity.

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To find the domain and range of the function ( f(x) = \sqrt{x - 2} ):

Domain:

- Since the square root function is defined for non-negative real numbers, the expression inside the square root (( x - 2 )) must be greater than or equal to zero.
- So, solve the inequality ( x - 2 \geq 0 ) to find the domain.
- ( x - 2 \geq 0 ) implies ( x \geq 2 ).
- Therefore, the domain of ( f(x) ) is all real numbers greater than or equal to 2, or in interval notation: ( [2, \infty) ).

Range:

- Since the square root function always returns non-negative values, the range of ( f(x) ) will be all non-negative real numbers.
- So, the range of ( f(x) ) is ( [0, \infty) ) in interval notation.

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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.

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.

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.

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