1 / 12

Chapter 8 Graphs, Relations, and Functions

Chapter 8 Graphs, Relations, and Functions. Section 6 Compound Inequalities. Section 8.6 Objectives. 1 Determine the Intersection or Union of Two Sets 2 Solve Compound Inequalities Involving “and” 3 Solve Compound Inequalities Involving “or” 4 Solve Problems Using Compound Inequalities.

zalika
Download Presentation

Chapter 8 Graphs, Relations, and Functions

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. Chapter 8 Graphs, Relations, and Functions Section 6 CompoundInequalities

  2. Section 8.6 Objectives 1 Determine the Intersection or Union of Two Sets 2 Solve Compound Inequalities Involving “and” 3 Solve Compound Inequalities Involving “or” 4 Solve Problems Using Compound Inequalities

  3. Implies intersection. 6 1 4 7 2 5 8 3 A B = {4, 5} Intersection of Sets The intersection of two sets A and B, denoted A B, is the set of all elements that belong to both set Aand set B. Let A = {1, 2, 3, 4, 5} and let B = {4, 5, 6, 7, 8}. A B

  4. Implies union. 8 1 2 4 3 10 5 6 Union of Sets The union of two sets A and B, denoted A B, is the set of all elements that are in the set Aor in the set B or in both A and B. Let A = {1, 2, 3, 4, 5, 6} and let B = {2, 4, 6, 8, 10}. A B AB = {1, 2, 3, 4, 5, 6, 8, 10}

  5. [ ) -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 Empty set Intersection and Union Example: Let A = {x| x 4} and B = {x| x < 1}. a.) Graph sets A and B on a number line. b.) Find A B and A  B. Write the solutions in interval notation. x 4 x< 1 A B =  or { } A  B = (– , 1) or [4, )

  6. – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x≤ –1 ] x≤ 4 ] ] Compound Inequalities Using “and” A compound inequalityis formed by joining two inequalities with the word “and” or “or”. Example: Solve the compound inequality and graph the solution set. x+ 3 ≤ 7 andx – 2 ≤ –3 x+ 3 ≤ 7 x – 2 ≤ –3 x≤ 4 x≤ –1 The solution set is {x| x≤ –1} or (– , –1].

  7. – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 ( ) ) ( Compound Inequalities Using “or” Example: Solve the compound inequality and graph the solution set. 6x 10 < 8 or 2x + 1 > 9 6x 10 < 8 2x + 1 > 9 6x < 18 2x > 8 x < 3 x > 4 The solution set is {x| x< 3 or x > 4} or (– , 3) or (4, ).

  8. Solving Compound Inequalities Steps for Solving Compound Inequalities Involving “and” Step 1: Solve each inequality separately. Step 2: Find the INTERSECTION of the solution sets of each inequality. Steps for Solving Compound Inequalities Involving “or” Step 1: Solve each inequality separately. Step 2: Find the UNION of the solution sets of each inequality.

  9. Get the variable by itself in the middle. The inequality signs are reversed. Solving Compound Inequalities Example: Solve the compound inequality.  3 <  4x + 1 < 17  4 <  4x < 16 Subtract 1 from all three parts. 1 > x >  4 Divide each part by  4. The solution set is {x|– 4 < x< 1} or (–4, 1).

  10. Compound Inequality Applications Example: Jeni needs to earn a C in her Statistics class. Her current test scores are 67, 72, 81, and 75. Her final exam is worth three test scores. In order to earn a C, Jeni’s average must lie between 70 and 79, inclusive. What range of scores can Jeni receive on the final exam and earn a C in the course? Step 1: Identify.We need to find the range of possible score for the final exam. This is a direct translation problem involving inequalities. Step 2: Name.Let x represent the final exam score. Continued.

  11. The final exam is worth 3 test scores. Compound Inequality Applications Example continued: Step 3: Translate.The average is calculated by adding up all of the test scores and dividing by the total number of scores. Step 4: Solve. Simplify. Multiply each part by 7. Subtract 295 from each part. Continued.

  12. Compound Inequality Applications Example continued: Divide each part by 3. Step 5: Check.Since x represents the final exam score, any score between 65 and 86, inclusive, should yield an average score between 70 and 79. Step 6: Answer the Question. Jeni must score between 65 and 86, inclusive on her final exam to earn a C average for the course.

More Related