# How do you find the domain and range of #f(x) = 5/(x-9)#?

The value that x cannot be is obtained by equating the denominator to zero and solving the function; otherwise, f(x) would become undefined.

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To find the domain of ( f(x) = \frac{5}{x - 9} ), set the denominator ( x - 9 ) not equal to zero and solve for ( x ): [ x - 9 \neq 0 ] [ x \neq 9 ]

So, the domain of ( f(x) ) is all real numbers except ( x = 9 ).

To find the range, note that the function is a rational function. Since the denominator can approach zero as ( x ) approaches 9, the function can take on arbitrarily large positive or negative values. Therefore, the range of ( f(x) ) is all real numbers except ( 0 ).

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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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