# What is the domain and range of #y= (4x^2 - 9) / ((2x+3)(x+1))#?

See below.

Notice:

Changing this in the numerator:

Removing similar factors:

This can be stated as follows in set notation:

or using interval notation:

To determine the range:

Thus, the range can be stated as follows:

or

This is evident from the function's graph:

graph{(2x-3)/(x+1) [-16.23, 16.25, -32.48, 32.44]}

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The domain of the function ( y = \frac{{4x^2 - 9}}{{(2x + 3)(x + 1)}} ) is all real numbers except ( x = -1 ) and ( x = -\frac{3}{2} ). The range is all real numbers except ( y = 4 ).

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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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- Consider #y = f(x) = (x-2) / (x+2)#, does this formula define a function for #-3<x< 3#?
- What is the domain and range of # y = 3(x-2)/x#?

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