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A rational function is a function that is formed by the ratio of two polynomials, where the numerator and the denominator are both polynomials. It is usually represented as: R(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials and x is the variable.

The domain of any function is the set of all possible input values (x-values) for which the function is defined. For a rational function, the domain includes all real numbers except those that make the denominator equal to zero. This is because division by zero is undefined in mathematics.

The denominator plays a critical role in determining the domain of a rational function. Since dividing by zero is not allowed, any x-value that makes the denominator zero must be excluded from the domain. Therefore, to find the domain of a rational function, we need to find the x-values that make the denominator equal to zero and exclude them from the domain.

Follow these steps to find the domain of a rational function: 1. Identify the denominator: Look at the function and determine the denominator polynomial, Q(x), which is the part that is being divided in the rational function. 2. Solve for zeros: Solve the equation Q(x) = 0 to find the x-values that would make the denominator equal to zero. This can be done using various methods such as factoring, using the quadratic formula, or other solving techniques depending on the polynomial. 3. Exclude zeros from the domain: The domain of the rational function will include all real numbers except the x-values that make the denominator zero. We will exclude any x-value found in Step 2 from the domain. By following these steps, the domain of any rational function can be found.