# Math Assignment Help With Domain Of The Rational Function

## 4.2 Domain of the rational function

The domain of a rational function is defined as those values of *x* for which the function is always defined and does not take the form of any indefinite form.

Now the roots of the denominator are obviously *x* = 4 and *x* = -3. That is, if *x* takes on either of these two values, the denominator becomes equal to zero. So the function is not defined for these two values of *x*. We say that the function is discontinuous at *x* = 4 and *x* = -3 and is continuous at all other values for *x*. In other words, all real numbers except 4 and -3 are allowed as inputs to this function.

The domain for the function, therefore, as expressed in interval notation is:

(-∞, -3) **U ** (-3, 4) **U **(4, + ∞)

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