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Warm-up

Warm-up. Determine the equation of this absolute value function. Then, give the intervals of increase and decrease and the domain and range. Math II Day 40 (10-7-09). UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s Question:

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Warm-up

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  1. Warm-up Determine the equation of this absolute value function. Then, give the intervals of increase and decrease and the domain and range.

  2. Math IIDay 40 (10-7-09) UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s Question: How do we solve absolute value inequalities? Standard: MM2A1.b,c

  3. 2.2 Solving Absolute Value Equations & Inequalities p. 28-32

  4. Absolute Value (of x) • Symbol lxl • The distance x is from 0 on the number line. • Always positive • Ex: l-3l=3 -4 -3 -2 -1 0 1 2

  5. Ex: x = 5 • What are the possible values of x? x = 5 or x = -5

  6. PracticeWorkbookPage 31 #1-9

  7. To solve an absolute value equation: ax+b = c, where c>0 (where c is positive) To solve, set up 2 new equations, then solve each equation. ax+b = c or ax+b = - c ** make sure the absolute value is by itself before you split to solve.

  8. Ex: Solve 6x-3 = 15 6x-3 = 15 or 6x-3 = -15 6x = 18 or 6x = -12 x = 3 or x = -2 * Plug in answers to check your solutions!

  9. Ex: Solve 2x + 7 -3 = 8 Get the abs. value part by itself first! 2x+7 = 11 Now split into 2 parts. 2x+7 = 11 or 2x+7 = -11 2x = 4 or 2x = -18 x = 2 or x = -9 Check the solutions.

  10. Your Turn: Solve 2x - 5 = 9

  11. To solve an absolute value inequality: ax+b < c or ax+b ≤ c, where c>0 To solve, set up a compound “and” inequality with –c and c and solve.

  12. Ex: Solve & graph. • Becomes an “and” problem -3 7 8

  13. To solve an absolute value inequality: ax+b > c or ax+b ≥ c, where c>0 To solve, set up a compound “or” inequality with -c and c and solve.

  14. Solve & graph. • Get absolute value by itself first. • Becomes an “or” problem -2 3 4

  15. Your Turn: Solve & graph.

  16. PracticeWorkbookpage 32 #21, 23

  17. PracticeWorkbookpage 32 #22, 24-29

  18. Assignmentpage 30 #7-25 (odd)

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