What is the domain and range of # y = (3(x-2))/x#?

Answer 1

#x inRR,x!=0,y inRR,y!=3#

The denominator of y cannot be zero as this would make y undefined.

#rArrx=0larrcolor(red)" excluded value"#
#"domain is " x inRR,x!=0#

To find any excluded value in the range, rearrange making x the subject.

#rArrxy=3x-6larrcolor(blue)" cross-multiply"#
#rArrxy-3x=-6larr" collect terms in x"#
#rArrx(y-3)=-6larr" common factor of x"#
#rArrx=-6/(y-3)#
#"the denominator cannot equal zero"#
#y-3=0rArry=3larrcolor(red)" excluded value"#
#"range is " y inRR,y!=3#
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Answer 2

The domain of the function ( y = \frac{3(x-2)}{x} ) is all real numbers except ( x = 0 ) because division by zero is undefined.

To find the range, we can analyze the behavior of the function as ( x ) approaches positive and negative infinity. As ( x ) approaches positive or negative infinity, ( y ) approaches 3. Therefore, the range of the function is all real numbers except ( y = 3 ).

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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.

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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