1 / 86

1.4 Absolute Values

Learn the definition and solve absolute value equations and inequalities. Discover compound absolute values and exponential rules. Dive into radicals, rational exponents, and conjugates for comprehensive math understanding.

ramonaw
Télécharger la présentation

1.4 Absolute Values

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. 1.4 Absolute Values Solving Absolute Value Equations By putting into one of 3 categories

  2. What is the definition of “Absolute Value”? __________________________________ __________________________________ Mathematically, ___________________ For example, in , where could x be? 0 3 -3

  3. To solve these situations, ______________________________________________________________________________________________________ Consider ________________________ 0

  4. That was Category 1 Category 1 : ____________________________ _______________________________________ _______________________________________ Example Case 1 Case 2

  5. Absolute Value Inequalities Think logically about another situation. What does mean? For instance, in the equation , _________________________________ 0

  6. How does that translate into a sentence? __________________________________ Now solve for x. This is Category 2: when x is less than a number

  7. Absolute Value Inequalities What does mean? In the equation , __________________________________ 0

  8. Less than = And statement Greater than = Or statement Note:  is the same as ; is the same as ; just have the sign in the rewritten equation match the original.

  9. Isolate Absolute Value • _______________________________________ • ______________________________________ • ______________________________________

  10. When x is on both sides • ______________________________________ ________________________________________ • ______________________________________ Case 1 Case 2

  11. Example inequality with x on other side Case 1 Case 2

  12. Examples Case 1 Case 2

  13. Case 1 Case 2

  14. Case 1 Case 2

  15. _________________________________ Whats wrong with this? ____________________________________________________________________________________

  16. 1-4 Compound Absolute ValuesEqualities and Inequalities More than one absolute value in the equation

  17. Some Vocab • Domain- _________________________ • Range- __________________________ • Restriction- _______________________ • __________________________________________________________________

  18. Find a number that works. We will find a more methodical approach to find all the solutions.

  19. In your approach, think about the values of this particular mathematical statement in the 3 different areas on a number line. • -_________________________________________ • ________________________________________ • - ________________________________________

  20. It now forms 3 different areas or cases on the number line. • ______________________________ • ______________________________ • ___________________________________

  21. Case 1 Domain ________________________ ____________________________________________________ ___________________________________________________________________________________________________

  22. Case 2 Domain ___________________________________

  23. Case 3 Domain _____________________________

  24. Final Answers • ______________________________ • ______________________________ • _____________________________ 2 5 -2

  25. If you get an answer in any of the cases where the variable disappears and the answer is TRUE ________________________________ ________________________________________________________________________________________________

  26. 1-5 Exponential Rules You know these already

  27. Review of the Basics

  28. Practice problems Simplify each expression

  29. Do NOT use calculators on the homework, please!! 

  30. 1-6 Radicals (Day 1) and Rational Exponents (Day 2)

  31. What is a Radical? In simplest term, it is a square root ( ) = ________________

  32. The Principle nth root of a: 1. • If a < 0 and n is odd then is a negative number ___________________ • If a < 0 and n is even, _____________ __________

  33. Vocab

  34. Lets Recall

  35. Rules of Radicals

  36. Practice problems Simplify each expression

  37. 1-6 Radicals (Day 1) and Rational Exponents (Day 2)

  38. What is a Rational Exponent? ____________________________________ ____________________________________ ____________________________________ ____________________________________

  39. Don’t be overwhelmed by fractions! These problems are not hard, as long as you remember what each letter means. Notice I used “p” as the numerator and “r” as the denominator. p= _____________________________ r= _____________________________ ________________________________________ ________________________________________ ________________________________________

  40. Practice problems Simplify each expression

  41. The last part of this topic What is wrong with this number? ___________________________________ ___________________________________ ___________________________________

  42. Rationalizing If you see a single radical in the denominator ______________________________________ ________________________________________ ________________________________________ ________________________________________

  43. Rationalizing If you see 1 or more radicals in a binomial, what can we do?

  44. What is a Conjugate? The conjugate of a + b ______. Why? The conjugate _______________________ ___________________________________ ___________________________________ ___________________________________

  45. Rationalizing Multiply top and bottom by the conjugate! Its MAGIC!!

  46. 1.7 Fundamental Operations

More Related