Click here to load reader

Absolute value function

  • View
    124

  • Download
    1

Embed Size (px)

Text of Absolute value function

  • 1. Absolute ValueFunctions Graphs andCompound Functions By: Jeffrey BivinLake Zurich High [email protected] Updated: November 15, 2006 Jeff Bivin -- LZHS

2. Absolute Value Functions Select the desired MENU option below Graphs 1. Translations2. Quick Graphs 3. Graphing Inequalities Writing as Compound Functions 4. Using the vertex and slopes 5. From DefinitionJeff Bivin -- LZHS 3. Absolute Value FunctionsTranslationsJeff Bivin -- LZHS 4. y =|x|Jeff Bivin -- LZHS 5. y = |x+1| + 2Jeff Bivin -- LZHS 6. y = |2x+5| - 4Jeff Bivin -- LZHS 7. y = 2 |x - 3| + 1Jeff Bivin -- LZHS 8. y = 3 |2x - 3| - 4Jeff Bivin -- LZHS 9. Absolute Value FunctionsQuick GraphsJeff Bivin -- LZHS 10. y =|x|Jeff Bivin -- LZHS 11. y = |x+1| + 2Jeff Bivin -- LZHS 12. y = |2x+5| - 4Jeff Bivin -- LZHS 13. y = 2 |x - 3| + 1Jeff Bivin -- LZHS 14. y = 3 |2x - 3| - 4Jeff Bivin -- LZHS 15. Absolute Value Functions Graphing InequalitiesJeff Bivin -- LZHS 16. y |2x+5| - 4Jeff Bivin -- LZHS 17. y > -2 |x - 3| + 1Jeff Bivin -- LZHS 18. y |x+1| + 2Jeff Bivin -- LZHS 19. y < -2 |3x + 4| + 1Jeff Bivin -- LZHS 20. y 3|-2x + 8| - 1Jeff Bivin -- LZHS 21. Absolute Value FunctionsWriting as Compound FunctionsusingVertex and slopesJeff Bivin -- LZHS 22. x+2=0 y=|x+2|x = 2 Slopes of sides x = 2x < 2x 2m=1Vertex (-2, 0) m = 1 m =1 left side right side( 2, 0) y 0 = 1( x ( 2 ) ) y 0 = 1( x (2) ) y = 1( x + 2 )y = 1( x + 2 ) y = x 2y=x+2 x + 2 , [ 2,+) y=Jeff Bivin -- LZHS x 2 , ( , 2) 23. y = 3| x - 4 | x4=0 x=4Slopes of sidesx=4 x 4 If x < 4x4=0y = 3( x 4 ) y = 3( x 4 ) x=4y = 3 x 12 y = 3 x + 12 3 x 12 , x4 y= 3 x + 12 , x < 4Jeff Bivin -- LZHS 30. y = -2| x + 1 |x = 2 x +1= 0If x > -1 If x < -1 x = 1y = 2( x + 1) y = 2( x + 1) y = 2x 2y = 2x + 2 2 x 2 , x 1y=2 x + 2 , x< 4Jeff Bivin -- LZHS 31. y = -3| 2x + 3 | + 1 x= 32If x >3 If x < 322x + 3 = 02 2x = 3y = 3( 2 x + 3) +1 y = (3)( 2 x + 3) +1x = 3 y = 6x 9 + 1 y = 3( 2 x + 3) +1 2 y = 6x 8 y = 6 x + 9 +1y = 6 x + 10 6 x 8 , x 32 y= 6 x + 10 , x