1. Table of Contents Rational Expressions and Functions where P(x) and Q(x) are polynomials, Q(x) ≠ 0. Example 1: The following are examples of rational expressions: A rational expression is given by

2. Table of Contents Note that 8x is a rational expression since it can be written in the form

3. Table of Contents A rational function is given by where P(x) and Q(x) are polynomials, Q(x) ≠ 0. The values of x for which Q(x) = 0 are called restricted values.

4. Table of Contents Example 2: Set the denominator equal to zero … … and solve. Determine the restricted values of the function. The restricted values are

5. Table of Contents The domain of a rational function is all real numbers except for the restricted values. Determine the domain of the function. Example 3: This is the same function of example #2, and the restricted values are

6. Table of Contents The domain of the function is all real numbers except for the restricted values. The domain can be written as:

7. Table of Contents Example 4: Set the denominator equal to zero … … and solve. Determine the domain of the function. The restricted values are

8. Table of Contents The domain of the function is all real numbers except for the restricted values. The domain can be written as:

9. Table of Contents Example 5: Set the denominator equal to zero. There is no real number for x that will make this equation true. Determine the domain of the function. Thus, there are no restricted values.

10. Table of Contents The domain of the function is all real numbers except for the restricted values. Since there are no restricted values, the domain can be written as:

11. Table of Contents