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Unit 2 - Rationals

Unit 2 - Rationals. By: Iman , Sarah, Simran & Sonali. Unit Overview. Zero and Negative Exponents Rational Exponents Rational Function Rational Variable Expressions (RVEs). Exponents. Zero: When a base is raised to a zero exponent , the answer is always 1 . Negative:

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Unit 2 - Rationals

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  1. Unit 2 - Rationals By: Iman, Sarah, Simran & Sonali

  2. Unit Overview • Zero and Negative Exponents • Rational Exponents • Rational Function • Rational Variable Expressions (RVEs)

  3. Exponents Zero: • When a base is raised to a zero exponent, the answer is always 1. Negative: • When a base is raised to a negative exponent, write the reciprocal of the base to a positive exponent.

  4. Zero Exponents Examples: • 20 • [(5)2)7]0 = 1 = (514)0 = 1

  5. Negative Exponents Examples: • 6-2 c) • (4-2)-1 = 42 = 16

  6. Rational Exponents • REMEMBER: Rational exponents are exponents in fraction form. • General form: • n is the index (always a positive number!) Power form → ← Radical Form

  7. Rational Exponents Example 1 – Write in radical form: • b)

  8. Rational Exponents Example 2 – Write in power form:

  9. The Rational Function • Base Function:

  10. Rational Function • Reminders: • Key points: (-1, -1), (1,1) • Asymptotes: • HA: y = 0 • VA: x = 0 What is an asymptote? A line that continually approaches the graph but never touches it. * Horizontal and vertical shifts change the location of the asymptotes!

  11. Rational Function Example 1 – Graph the following function:

  12. Rational Function - Continued

  13. Rational Variable Expressions • An RVE is a quotient where the numerator and denominator are both polynomials. • Example:

  14. Rational Variable Expressions • An RVE is only defined when the denominator DOES NOT equal 0. This is where we have restrictions! • Example: • Note: A hole exists in the graph when the restrictions are reduced away! ↑ These values of x set the denominator to 0.

  15. Rational Variable Expressions Examples – Simplify the following RVEs:

  16. Applications of Rationals Example 1: Write & simplify an expression that represents the area of the following triangle.

  17. Math Bingo! • Answer the questions on the following slides • Cross off the correct answers on the bingo card provided (use pencil!) • Winners will receive prizes!

  18. 1. What restrictions exist?

  19. 2. When a base is raised to a zero exponent,what is the answer?

  20. 3. What does RVE stand for? • Rational Variable Exponent • Rational Variable Expression • Rational Variety Expressions

  21. 4. What do you state restrictions on? • Denominator • Numerator • Both a) and b)

  22. 5. What would the vertical asymptote be? a) VA: x = 3 c) VA: x = -3 b) VA: y = -3

  23. 6. What would the horizontal asymptote be? • HA: y = -5 • HA: y = 5 • HA: y = 2 • HA: y = -2

  24. 7. The following is a function: • TRUE or FALSE

  25. 8. What are the base points of a rational function? • (5,5), (-5,-6) • (1,3), (-70,-72) • (1,1), (-1, -2) • (1,1), (-6, -9) • None of the above

  26. 9. TRUE OR FALSE: Horizontal and vertical shifts change the location of the key points.

  27. 10. What exists in the graph when restrictions are reduced away?

  28. Answers to Bingo Qs: • Cannot equal 0,4 • 1 • Rational Variable Expression • Denominator • VA: x = -3 • HA: y = -2 • True (it’s the rational function!!) • None of the above (Correct answer: (-1,1), (1,1) • True • Holes

  29. Homefun!! Start the Rationals Practice Questions and review Unit 3’s Study Sheet! ☺

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