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Absolute value function

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Jeff Bivin -- LZHS Absolute Value Functions Graphs and Compound Functions By: Jeffrey Bivin Lake Zurich High School [email protected] Last Updated: November 15, 2006
Transcript
Page 1: Absolute value function

Jeff Bivin -- LZHS

Absolute Value Functions

Graphsand

Compound Functions

By: Jeffrey Bivin

Lake Zurich High School

[email protected]

Last Updated: November 15, 2006

Page 2: Absolute value function

Jeff Bivin -- LZHS

Absolute Value Functions

Select the desired MENU option below

Graphs1. Translations

2. Quick Graphs

3. Graphing Inequalities

Writing as Compound Functions4. Using the vertex and slopes

5. From Definition

Page 3: Absolute value function

Jeff Bivin -- LZHS

Absolute Value Functions

Translations

Page 4: Absolute value function

Jeff Bivin -- LZHS

y =|x|

Page 5: Absolute value function

Jeff Bivin -- LZHS

y = |x+1| + 2

Page 6: Absolute value function

Jeff Bivin -- LZHS

y = |2x+5| - 4

Page 7: Absolute value function

Jeff Bivin -- LZHS

y = 2 |x - 3| + 1

Page 8: Absolute value function

Jeff Bivin -- LZHS

y = 3 |2x - 3| - 4

Page 9: Absolute value function

Jeff Bivin -- LZHS

Absolute Value Functions

Quick Graphs

Page 10: Absolute value function

Jeff Bivin -- LZHS

y =|x|

Page 11: Absolute value function

Jeff Bivin -- LZHS

y = |x+1| + 2

Page 12: Absolute value function

Jeff Bivin -- LZHS

y = |2x+5| - 4

Page 13: Absolute value function

Jeff Bivin -- LZHS

y = 2 |x - 3| + 1

Page 14: Absolute value function

Jeff Bivin -- LZHS

y = 3 |2x - 3| - 4

Page 15: Absolute value function

Jeff Bivin -- LZHS

Absolute Value Functions

Graphing Inequalities

Page 16: Absolute value function

Jeff Bivin -- LZHS

y ≤ |2x+5| - 4

Page 17: Absolute value function

Jeff Bivin -- LZHS

y > -2 |x - 3| + 1

Page 18: Absolute value function

Jeff Bivin -- LZHS

y ≥ |x+1| + 2

Page 19: Absolute value function

Jeff Bivin -- LZHS

y < -2 |3x + 4| + 1

Page 20: Absolute value function

Jeff Bivin -- LZHS

y ≥ 3|-2x + 8| - 1

Page 21: Absolute value function

Jeff Bivin -- LZHS

Absolute Value Functions

Writing as

Compound Functions

using

Vertex and slopes

Page 22: Absolute value function

Jeff Bivin -- LZHS

y = | x + 2 | 02 x2x

)2(10 xy

2xy 21 xy

2 xy

2,,2

,2,2

x

xy

0,2

Vertex (-2, 0)

Slopes of sides

m = ± 1

right side

1m1m

21 xy

left side

210 xy

2x2x 2x

Page 23: Absolute value function

Jeff Bivin -- LZHS

y = 3| x - 4 | 04 x4x

430 xy123 xy123 xy

4,,123

,4,123

x

xy

0,4

Vertex (4, 0)

Slopes of sides

m = ± 3

right side

3m3m

left side

430 xy

4x4x 4x

Page 24: Absolute value function

Jeff Bivin -- LZHS

y = -2| x + 1 | 01x1x

)1(20 xy 12 xy

22 xy

1,,22

,1,22

x

xy

0,1

Vertex

Slopes of sides

m = ± 2

right side

2m2m

left side

)1(20 xy

1x1x

1x

22 xy

12 xy

0,1

Page 25: Absolute value function

Jeff Bivin -- LZHS

y = 2| x - 5 | +3 05 x5x

523 xy1023 xy

132 xy

,5,72

5,,132

x

xy

3,5

Vertex (5, 3)

Slopes of sides

m = ± 2

right side

2m2m

left side

523 xy

5x5x 5x

72 xy

1023 xy

Page 26: Absolute value function

Jeff Bivin -- LZHS

y = -4| 2x - 5 | + 7 052 x52 x

2587 xy2087 xy

138 xy

25

25

,,138

,,278

x

xy

7,25

Vertex

Slopes of sides

m = ± 8

right side

8m8m

left side

2587 xy

25x

25x

25x

278 xy

2087 xy

25x

7,25

Page 27: Absolute value function

Jeff Bivin -- LZHS

Absolute Value Functions

Writing as

Compound Functions

From Definition

Page 28: Absolute value function

Jeff Bivin -- LZHS

y = | x + 2 |

02 x

2x

If x > -2

2 xy

2xy

If x < -2

2 xy

2 xy

2,2

2,2

xx

xxy

2x

Page 29: Absolute value function

Jeff Bivin -- LZHS

y = 3| x - 4 |

04 x

4x

If x > 4

43 xy

123 xy

If x < 4

43 xy

123 xy

4,123

4,123

xx

xxy

4x

Page 30: Absolute value function

Jeff Bivin -- LZHS

y = -2| x + 1 |

01x

1xIf x > -1

12 xy

22 xy

If x < -1

12 xy

22 xy

4,22

1,22

xx

xxy

2x

Page 31: Absolute value function

Jeff Bivin -- LZHS

y = -3| 2x + 3 | + 1

032 x32 x 1323 xy

196 xy 132)3( xy

1)32(3 xy

23

23

,106

,86

xx

xxy

23x

23x

23xIf 2

3xIf

86 xy 196 xy106 xy


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