# How do you find the domain and range of #y = 3(x-2)/x#?

Domain:

Range:

Therefore, the inverse function will be

graph{(3(x-2))/x [-10, 10, 5, 5, 10]}

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To find the domain of the function ( y = \frac{3(x-2)}{x} ), we need to identify any values of ( x ) that would make the denominator ( x ) equal to zero. Since division by zero is undefined, the domain is all real numbers except for ( x = 0 ). So, the domain is ( x \neq 0 ).

To find the range, we need to analyze the behavior of the function as ( x ) approaches positive infinity and negative infinity. As ( x ) approaches positive infinity, the term ( (x - 2) ) becomes negligible compared to ( x ), so ( y ) approaches ( 3 ). Similarly, as ( x ) approaches negative infinity, ( y ) also approaches ( 3 ). Therefore, the range of the function is all real numbers except ( y = 3 ). So, the range is ( y \neq 3 ).

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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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