11x1 t03 04 absolute value (2011)
TRANSCRIPT
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*