# For #f(x) = 1/(x-3)#, what is the natural domain and range?

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The natural domain of the function ( f(x) = \frac{1}{x-3} ) is all real numbers except ( x = 3 ) because division by zero is undefined.

The range of the function ( f(x) = \frac{1}{x-3} ) is all real numbers except ( y = 0 ) because the function will never output zero for any value of ( x ) due to the denominator never being zero (except when ( x = 3 ), which is excluded from the domain).

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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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