11 x1 t03 04 absolute value (2012)

Absolute Value

Absolute Value, 0

, 0a a

aa a

Absolute Value, 0

, 0a a

aa a

Absolute value is distance of a number from 0.

Absolute Value, 0

, 0a a

aa a

Absolute value is distance of a number from 0.It is magnitude only, direction is NOT considered.

Absolute Value, 0

, 0a a

aa a

Absolute value is distance of a number from 0.

e.g. 5i

It is magnitude only, direction is NOT considered.

Absolute Value, 0

, 0a a

aa a

Absolute value is distance of a number from 0.

e.g. 5i 5

It is magnitude only, direction is NOT considered.

Absolute Value, 0

, 0a a

aa a

Absolute value is distance of a number from 0.

e.g. 5i 5

( ) 6 8 2ii

It is magnitude only, direction is NOT considered.

Absolute Value, 0

, 0a a

aa a

Absolute value is distance of a number from 0.

e.g. 5i 5

( ) 6 8 2ii 4

It is magnitude only, direction is NOT considered.

4

Absolute Value, 0

, 0a a

aa a

Absolute value is distance of a number from 0.

e.g. 5i 5

( ) 6 8 2ii 4

It is magnitude only, direction is NOT considered.

4

( )7 6 3 20iii

Absolute Value, 0

, 0a a

aa a

Absolute value is distance of a number from 0.

e.g. 5i 5

( ) 6 8 2ii 4

It is magnitude only, direction is NOT considered.

4

( )7 6 3 20iii 7 2 7 25

Absolute Value, 0

, 0a a

aa a

Absolute value is distance of a number from 0.

e.g. 5i 5

( ) 6 8 2ii 4

It is magnitude only, direction is NOT considered.

4

( )7 6 3 20iii 7 2 7 25

( )3 6iv

Absolute Value, 0

, 0a a

aa a

Absolute value is distance of a number from 0.

e.g. 5i 5

( ) 6 8 2ii 4

It is magnitude only, direction is NOT considered.

4

( )7 6 3 20iii 7 2 7 25

( )3 6iv 3 6 18

Absolute Value Equations/Inequations

Absolute Value Equations/Inequations

e.g. 7i x

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

2 105

xx

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

2 105

xx

2 3 72 4

2

xxx

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

2 105

xx

2 3 72 4

2

xxx

2 or 5x x

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

2 105

xx

2 3 72 4

2

xxx

2 or 5x x

( ) 2 6 3 1iii x x

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

2 105

xx

2 3 72 4

2

xxx

2 or 5x x

( ) 2 6 3 1iii x x

2 6 3 1 or 2 6 3 1x x x x

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

2 105

xx

2 3 72 4

2

xxx

2 or 5x x

( ) 2 6 3 1iii x x

2 6 3 1 or 2 6 3 1x x x x 7

7xx

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

2 105

xx

2 3 72 4

2

xxx

2 or 5x x

( ) 2 6 3 1iii x x

2 6 3 1 or 2 6 3 1x x x x 7

7xx

2 6 3 15 5

1

x xxx

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

2 105

xx

2 3 72 4

2

xxx

2 or 5x x

( ) 2 6 3 1iii x x

2 6 3 1 or 2 6 3 1x x x x 7

7xx

2 6 3 15 5

1

x xxx

(NOT a solution)

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

2 105

xx

2 3 72 4

2

xxx

2 or 5x x

( ) 2 6 3 1iii x x

2 6 3 1 or 2 6 3 1x x x x 7

7xx

2 6 3 15 5

1

x xxx

(NOT a solution)

7x

Absolute Value Equations/Inequations

e.g. 7i x 7 or 7x x

( ) 2 3 7ii x 2 3 7 or 2 3 7x x

2 105

xx

2 3 72 4

2

xxx

2 or 5x x

( ) 2 6 3 1iii x x

2 6 3 1 or 2 6 3 1x x x x 7

7xx

2 6 3 15 5

1

x xxx

(NOT a solution)

7x

:

Note the equationsomething with pronumerals

may produce an answer thatis not a solution

( ) 5 2iv x

( ) 5 2iv x

5 2 or 5 2x x

( ) 5 2iv x

5 2 or 5 2x x 3x

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

–7 –3

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

–7 –3

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

–7 –37 3x

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

–7 –37 3x

( ) 3 2 1v x

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

–7 –37 3x

( ) 3 2 1v x

3 2 1 or 3 2 1x x

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

–7 –37 3x

( ) 3 2 1v x

3 2 1 or 3 2 1x x

3 113

x

x

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

–7 –37 3x

( ) 3 2 1v x

3 2 1 or 3 2 1x x

3 113

x

x

3 2 13 3

1

xxx

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

–7 –37 3x

( ) 3 2 1v x

3 2 1 or 3 2 1x x

3 113

x

x

3 2 13 3

1

xxx

–1 13

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

–7 –37 3x

( ) 3 2 1v x

3 2 1 or 3 2 1x x

3 113

x

x

3 2 13 3

1

xxx

–1 13

( ) 5 2iv x

5 2 or 5 2x x 3x 5 2

77

xxx

–7 –37 3x

( ) 3 2 1v x

3 2 1 or 3 2 1x x

3 113

x

x

3 2 13 3

1

xxx

–1 13

11 or 3

x x

Absolute Value Graphs

Absolute Value Graphs

y f x

the part of below the axis is reflected above the axisf x x x

Absolute Value Graphs

y f x

the part of below the axis is reflected above the axisf x x x

y f x

the left side of ( ) disappears and the right side is reflected in the axisf x y

Absolute Value Graphs

y f x

the part of below the axis is reflected above the axisf x x x

y f x

the left side of ( ) disappears and the right side is reflected in the axisf x y

e.g. i y x

Absolute Value Graphs

y f x

the part of below the axis is reflected above the axisf x x x

y f x

the left side of ( ) disappears and the right side is reflected in the axisf x y

e.g. i y xy

x

Absolute Value Graphs

y f x

the part of below the axis is reflected above the axisf x x x

y f x

the left side of ( ) disappears and the right side is reflected in the axisf x y

e.g. i y xy

x

(1,1)(–1,1)

( ) 2ii y x

( ) 2ii y x y

x

1. : basic curve y x

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units 2

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units –2

(–1,1)(–3,1)

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units –2OR

1. : 2basic curve y x

2

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units –2OR

1. : 2basic curve y x

2

2. reflect up in the x axis

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units –2OR

1. : 2basic curve y x

2

2. reflect up in the x axis

(–1,1)(–3,1)

( ) 2iii y x

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units –2OR

1. : 2basic curve y x

2

2. reflect up in the x axis

(–1,1)(–3,1)

( ) 2iii y x

y

x

1. : basic curve y x

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units –2OR

1. : 2basic curve y x

2

2. reflect up in the x axis

(–1,1)(–3,1)

( ) 2iii y x

y

x

1. : basic curve y x

2. shift up 2 units

2

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units –2OR

1. : 2basic curve y x

2

2. reflect up in the x axis

(–1,1)(–3,1)

( ) 2iii y x

y

x

1. : basic curve y x

2. shift up 2 units 2

(1,3)(–1,3)

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units –2OR

1. : 2basic curve y x

2

2. reflect up in the x axis

(–1,1)(–3,1)

( ) 2iii y x

y

x

1. : basic curve y x

2. shift up 2 units 2OR

1. : 2basic curve y x

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units –2OR

1. : 2basic curve y x

2

2. reflect up in the x axis

(–1,1)(–3,1)

( ) 2iii y x

y

x

1. : basic curve y x

2. shift up 2 units 2OR

1. : 2basic curve y x

2. reflect left in the y axis

( ) 2ii y x y

x

1. : basic curve y x

2. shift left 2 units –2OR

1. : 2basic curve y x

2

2. reflect up in the x axis

(–1,1)(–3,1)

( ) 2iii y x

y

x

1. : basic curve y x

2. shift up 2 units 2OR

1. : 2basic curve y x

2. reflect left in the y axis

(1,3)(–1,3)

2( ) 2iv y x

2( ) 2iv y x y

x

21. : 2basic curve y x

–22 2

2( ) 2iv y x y

x

21. : 2basic curve y x

2 22. reflect up in the x axis

2

2( ) 2iv y x y

x

21. : 2basic curve y x

2 22. reflect up in the x axis

2

( ) 5 2v x

2( ) 2iv y x y

x

21. : 2basic curve y x

2 22. reflect up in the x axis

2

( ) 5 2v x

y

x–5

5 5y x

2( ) 2iv y x y

x

21. : 2basic curve y x

2 22. reflect up in the x axis

2

( ) 5 2v x

y

x–5

5 5y x

2y

2( ) 2iv y x y

x

21. : 2basic curve y x

2 22. reflect up in the x axis

2

( ) 5 2v x

y

x–5

5(–3,2)(–7,2)

5y x

2y

2( ) 2iv y x y

x

21. : 2basic curve y x

2 22. reflect up in the x axis

2

( ) 5 2v x

y

x–5

5(–3,2)(–7,2)

5y x

2y

Q: for what values of x is theabsolute value curve below the line y = 2?

2( ) 2iv y x y

x

21. : 2basic curve y x

2 22. reflect up in the x axis

2

( ) 5 2v x

y

x–5

5(–3,2)(–7,2)

5y x

2y

Q: for what values of x is theabsolute value curve below the line y = 2?

7 3x

2( ) 2iv y x y

x

21. : 2basic curve y x

2 22. reflect up in the x axis

2

( ) 5 2v x

y

x–5

5(–3,2)(–7,2)

5y x

2y

Q: for what values of x is theabsolute value curve below the line y = 2?

7 3x

Exercise 3D; 2acfh, 3bdfh, 5adfh,7bd, 8bdf, 9b i, iii, 11, 14, 18, 21*

Exercise 3E; 1, 2ab, 3ac, 4ac, 5ac,14, 17c, 20*