![y = 2| x - 5 | +3
x −5=0 x =5 Slopes of sides
x =5 x<5 x≥5
m=±2
Vertex (5, 3) m = −2 m=2
left side right side
( 5, 3)
y − 3 = − 2( x − 5) y − 3 = 2( x − 5)
y − 3 = − 2 x + 10 y − 3 = 2 x − 10
y = − 2 x + 13 y = 2x − 7
− 2 x + 13 , ( − ∞, 5]
y=
Jeff Bivin -- LZHS
2 x − 7 , ( 5, + ∞)](https://image.slidesharecdn.com/absolutevaluefunction-130124022630-phpapp01/85/Absolute-value-function-25-320.jpg)
![y = -4| 2x - 5 | + 7
2x − 5 = 0 ( 5 , 7)
2 Slopes of sides
2x = 5 m=±8
x=5 2
m =8 m = −8
Vertex ( 5
2 , 7) x< 5
2
x≥ 5
2
left side x= 5 right side
2
y − 7 = 8( x − 5 )
2 y − 7 = − 8( x − 5 )
2
y − 7 = 8 x − 20 y − 7 = − 8 x + 20
y = 8 x − 13 y = − 8 x + 27
− 8 x + 27 , ( 5 , + ∞)
2
y=
Jeff Bivin -- LZHS
8 x −13 , ( − ∞, 2 ]
5](https://image.slidesharecdn.com/absolutevaluefunction-130124022630-phpapp01/85/Absolute-value-function-26-320.jpg)
Absolute value function
- 1. Absolute Value Functions Graphs and Compound Functions By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: November 15, 2006 Jeff Bivin -- LZHS
- 2. Absolute Value Functions Select the desired MENU option below Graphs 1. Translations 2. Quick Graphs 3. Graphing Inequalities Writing as Compound Functions 4. Using the vertex and slopes 5. From Definition Jeff Bivin -- LZHS
- 3. Absolute Value Functions Translations Jeff Bivin -- LZHS
- 4. y =|x| Jeff Bivin -- LZHS
- 5. y = |x+1| + 2 Jeff Bivin -- LZHS
- 6. y = |2x+5| - 4 Jeff Bivin -- LZHS
- 7. y = 2 |x - 3| + 1 Jeff Bivin -- LZHS
- 8. y = 3 |2x - 3| - 4 Jeff Bivin -- LZHS
- 9. Absolute Value Functions Quick Graphs Jeff Bivin -- LZHS
- 10. y =|x| Jeff Bivin -- LZHS
- 11. y = |x+1| + 2 Jeff Bivin -- LZHS
- 12. y = |2x+5| - 4 Jeff Bivin -- LZHS
- 13. y = 2 |x - 3| + 1 Jeff Bivin -- LZHS
- 14. y = 3 |2x - 3| - 4 Jeff Bivin -- LZHS
- 15. Absolute Value Functions Graphing Inequalities Jeff Bivin -- LZHS
- 16. y ≤ |2x+5| - 4 Jeff Bivin -- LZHS
- 17. y > -2 |x - 3| + 1 Jeff Bivin -- LZHS
- 18. y ≥ |x+1| + 2 Jeff Bivin -- LZHS
- 19. y < -2 |3x + 4| + 1 Jeff Bivin -- LZHS
- 20. y ≥ 3|-2x + 8| - 1 Jeff Bivin -- LZHS
- 21. Absolute Value Functions Writing as Compound Functions using Vertex and slopes Jeff Bivin -- LZHS
- 22. x+2=0 y=|x+2| x = −2 Slopes of sides x = −2 x < −2 x ≥ −2 m=±1 Vertex (-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 − 2 y=x+2 x + 2 , [ − 2,+∞) y= Jeff Bivin -- LZHS − x − 2 , ( − ∞, − 2)
- 23. y = 3| x - 4 | x−4=0 x=4 Slopes of sides x=4 x<4 x≥4 m=±3 Vertex (4, 0) m = −3 m=3 left side right side ( 4, 0) y − 0 = − 3( x − 4 ) y − 0 = 3( x − 4 ) y = − 3 x + 12 y = 3 x − 12 3 x −12 , [ 4, + ∞) y= Jeff Bivin -- LZHS − 3 x + 12 , ( − ∞, 4)
- 24. y = -2| x + 1 | x +1= 0 ( −1, 0) Slopes of sides x = −1 m=±2 m=2 m = −2 Vertex ( −1, 0 ) x < −1 x ≥ −1 left side x = −1 right side y − 0 = 2( x − (−1) ) y − 0 = − 2( x − (−1) ) y = 2( x + 1) y = − 2( x + 1) y = 2x + 2 y = − 2x − 2 − 2 x − 2 , [ −1, + ∞) y= Jeff Bivin -- LZHS 2x + 2 , ( − ∞, −1)
- 25. y = 2| x - 5 | +3 x −5=0 x =5 Slopes of sides x =5 x<5 x≥5 m=±2 Vertex (5, 3) m = −2 m=2 left side right side ( 5, 3) y − 3 = − 2( x − 5) y − 3 = 2( x − 5) y − 3 = − 2 x + 10 y − 3 = 2 x − 10 y = − 2 x + 13 y = 2x − 7 − 2 x + 13 , ( − ∞, 5] y= Jeff Bivin -- LZHS 2 x − 7 , ( 5, + ∞)
- 26. y = -4| 2x - 5 | + 7 2x − 5 = 0 ( 5 , 7) 2 Slopes of sides 2x = 5 m=±8 x=5 2 m =8 m = −8 Vertex ( 5 2 , 7) x< 5 2 x≥ 5 2 left side x= 5 right side 2 y − 7 = 8( x − 5 ) 2 y − 7 = − 8( x − 5 ) 2 y − 7 = 8 x − 20 y − 7 = − 8 x + 20 y = 8 x − 13 y = − 8 x + 27 − 8 x + 27 , ( 5 , + ∞) 2 y= Jeff Bivin -- LZHS 8 x −13 , ( − ∞, 2 ] 5
- 27. Absolute Value Functions Writing as Compound Functions From Definition Jeff Bivin -- LZHS
- 28. x = −2 y=|x+2| If x > -2 If x < -2 x+2=0 y = ( x + 2) y = − ( x + 2) x = −2 y=x+2 y = −x − 2 x + 2 , x ≥ −2 y= − x − 2 , x < − 2 Jeff Bivin -- LZHS
- 29. x=4 y = 3| x - 4 | If x > 4 If x < 4 x−4=0 y = 3( x − 4 ) y = − 3( x − 4 ) x=4 y = 3 x − 12 y = − 3 x + 12 3 x − 12 , x≥4 y= − 3 x + 12 , x < 4 Jeff Bivin -- LZHS
- 30. y = -2| x + 1 | x = −2 x +1= 0 If x > -1 If x < -1 x = −1 y = − 2( x + 1) y = 2( x + 1) y = − 2x − 2 y = 2x + 2 − 2 x − 2 , x ≥ −1 y= 2 x + 2 , x< 4 Jeff Bivin -- LZHS
- 31. y = -3| 2x + 3 | + 1 x= −3 2 If x > −3 If x < −3 2 2x + 3 = 0 2 2x = − 3 y = − 3( 2 x + 3) +1 y = − (−3)( 2 x + 3) +1 x = −3 y = − 6x − 9 + 1 y = 3( 2 x + 3) +1 2 y = − 6x − 8 y = 6 x + 9 +1 y = 6 x + 10 − 6 x − 8 , x ≥ −3 2 y= 6 x + 10 , x < −3 2 Jeff Bivin -- LZHS