1. Rational Functions and Domains where P(x) and Q(x) are polynomials, Q(x) ≠ 0. A rational expression is given by

2. Example 1 The following are examples of rational expressions: Note that 8x is a rational expression since it can be written in the form

3. A rational function is given by where P(x) and Q(x) are polynomials, Q(x) ≠ 0.

4. Example 2 The following are examples of rational functions:

5. The domain of a rational function is all real numbers except for those values for which the denominator is zero. To find the domain of a rational function 1.Set the denominator to zero and solve 2.The domain is all real numbers except for the solutions found in step 1

6. Example 3 Set the denominator equal to zero … … and solve. Determine the domain of the function.

7. The solutions are Dom f : All real numbers, In interval notation

8. Example 4: Set the denominator equal to zero … … and solve. Determine the domain of the function.

9. The solutions are Dom f : All real numbers, In interval notation

10. 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.

11. Dom f : All real numbers In interval notation