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

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Presentation transcript:

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

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

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

Example 2 The following are examples of rational functions:

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

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

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

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

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

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.

Dom f : All real numbers In interval notation