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Mastering Rationals: Exploring Functions and Equations

Dive deep into rational functions, inverse variation, and complex fractions. Learn to solve rational equations and tackle addition and subtraction of rationals with ease. Practice identifying asymptotes and graphing functions.

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Mastering Rationals: Exploring Functions and Equations

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  1. Adding and Subtracting Rationals

  2. Review

  3. Review • Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero.

  4. Review • Inverse Variation Function - Graph

  5. Review • Rational Functions - Asymptotes

  6. Review • Rational Functions - Asymptotes

  7. Review • Rational Functions – Sketching the graph Draw all the asymptotes Determine where it is positive and negative Determine where it is Zero Sketch

  8. Review • Rational Expressions – Multiplication / Division Restrictions – When the denominator is zero When dividing by zero Simplify by canceling like terms (factors)

  9. New Material

  10. Addition Subtraction Rationals

  11. Addition Subtraction Rationals

  12. Addition Subtraction Rationals

  13. Addition Subtraction Rationals

  14. Addition Subtraction Rationals

  15. Addition Subtraction Rationals

  16. Addition Subtraction Rationals

  17. Addition Subtraction Rationals

  18. Addition Subtraction Rationals

  19. Addition Subtraction Rationals • Complex Fractions – A fraction that has a fraction in the numerator or denominator

  20. Addition Subtraction Rationals

  21. Addition Subtraction Rationals

  22. Addition Subtraction Rationals

  23. Solving Rational Equations

  24. Solving Rational Equations • Multiplying variables on both sides of an equal sign may introduce extraneous solutions. • Check for extraneous solutions by plugging into the original equation.

  25. Solving Rational Equations

  26. Solving Rational Equations

  27. Solving Rational Equations - Practice

  28. Solving Rational Equations • If rational functions are added in an equation, use the LCD to multiply all terms and “clear” the fraction

  29. Solving Rational Equations – Example

  30. Solving Rational Equations – Example

  31. Solving Rational Equations - Practice

  32. Solving Rational Equations – Example

  33. Solving Rational Equations - Practice

  34. Homework • 9-5 Adding and Subtracting Rationals First Column • 9-6 Solving Rational Expressions First Column End at #38

  35. Homework • 9-5 Adding and Subtracting Rationals First Column

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