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Rational Functions and Domains

Rational Functions and Domains. A rational expression is given by. where P(x) and Q(x) are polynomials, Q(x) ≠ 0. Example 1. The following are examples of rational expressions:. Note that 8x is a rational expression since it can be written in the form.

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Rational Functions and Domains

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

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

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

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

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

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

  10. Example 5: Determine the domain of the function. Set the denominator equal to zero. There is no real number for x that will make this equation true.

  11. Dom f : All real numbers In interval notation

  12. END OF PRESENTATION

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