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

Answer 1

See below

The domain is all the values that #x# is allowed to take on. The only problem I have with this function is that I need to be careful not to divide by zero. So the only values that x can not take on are those which would cause division by zero. So I'll set the denominator equal to zero and solve; my domain will be everything else.

#x+2=0# #x=-2#

So the domain of this function is everything from positive infinity to negative infinity except #-2#.

The range is all the values that #y# will take on. In this case, the range is all x.

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Answer 2

Isaiah Anthony

Domain: ( x \neq -2 )
Range: All real numbers except 2

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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.