noleta
Uploaded by
29 SLIDES
447 VUES
300LIKES

Understanding Rationals: Exponents, Functions, and Variable Expressions

DESCRIPTION

Dive into the world of rational numbers with our comprehensive overview. This unit covers essential topics, including zero and negative exponents, rational exponents, rational functions, and rational variable expressions (RVEs). Learn how to interpret and manipulate different exponents, understand asymptotes in rational functions, and simplify various RVEs. Utilize engaging examples and applications to grasp these fundamental concepts effectively. Join our interactive "Math Bingo!" to solidify your knowledge and have fun while learning about rational expressions and their significance in mathematics.

1 / 29

Télécharger la présentation

Understanding Rationals: Exponents, Functions, and Variable Expressions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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! ☺

More Related