How do you find the domain for a rational function?

To identify the domain of a rational function, it's essential to focus on the behavior of the function in relation to its denominator. A rational function is of the form ( f(x) = \frac{P(x)}{Q(x)} ), where ( P(x) ) is the numerator and ( Q(x) ) is the denominator. The key point is that the function is undefined whenever the denominator equals zero, as division by zero is not permissible in mathematics.

Thus, to determine the domain, one must exclude any values of ( x ) that result in the denominator ( Q(x) ) being zero. This ensures that the function remains defined and valid for all acceptable ( x ) values. As a result, the correct answer highlights the necessity of omitting those specific numbers from the domain to maintain the function's validity.

Including all real numbers or only excluding negative numbers would not appropriately account for the conditions necessary for the rational function to be well-defined. Therefore, recognizing that the numerator being zero does not restrict the domain, while the denominator being zero does, confirms the accuracy of focusing on the denominator to find the domain of a rational function.