Date post: | 18-Jan-2016 |
Category: |
Documents |
Upload: | donna-miles |
View: | 216 times |
Download: | 0 times |
Absolute ValuesReview
Defn: A non-directional distance from zero.
Absolute values are always non-negative.
Does not exist.
4x x 4 4, and
21x x 21 21, and
7x
Absolute ValuesAbsolute Values of Expression
What value(s) of x will make the expression equal to 8 or -8?
843 x
123 x 43 x
843 x843 x
3
4x4x
4,3
4: xsolution
Absolute ValuesAbsolute Values of Expressions
What value(s) of x will make the expression equal to 7 or -7?
735 x
45 x 105 x
735 x735 x
2x5
4x
2,5
4: xsolution
Absolute ValuesAbsolute Values of Expressions
What value(s) of x will make the expression equal to 0?
032 x
32 x
032 x
2
3x
Absolute ValuesAbsolute Values of Expressions
What value(s) of x will make the expression equal to -1?
166 x
56 x
166 x
6
5x
166
56
165
11
11
No solution
166 x
166 x
6
7x
76 x
166
76
167
11
11
No solution
Absolute ValuesAbsolute Values of Inequalities
What value(s) of x will make the inequality greater than or equal to 8?
843 x
123 x
843 x
4x
843 x
843 x
43 x
3
4xInterval Notation
,4
3
4,
Absolute ValuesAbsolute Values of Inequalities
What value(s) of x will make the inequality greater than or equal to 8?
843 x
123 x
843 x
4x
843 x
843 x
43 x
3
4xInterval Notation
4,
3
4
Absolute ValuesAbsolute Values of Other Inequalities
2432 x
33 x
632 x
33 x
6x
Interval Notation
,60,
33 x
33 x
0x
Absolute ValuesAbsolute Values of Other Inequalities
532 xx
82 xx
532 xx
8x23 x
3
2x
532 xx
532 xx
22 xx
Graphs, Relations, and FunctionsDefn: A relation is a set of ordered pairs.
2,4,2,4,1,1,1,1,0,0 A
:Arange
4,1,0
2,1,0,1,2
Domain: The values of the 1st component of the ordered pair.
:Adomain
Range: The values of the 2nd component of the ordered pair.
The Rectangular Coordinate System Ordered Pair
(x, y)
(independent variable, dependent variable)
(1st component, 2nd component)
(input, output)
(abscissa, ordinate)
x
y
1st Quadrant2nd Quadrant
3rd Quadrant 4th Quadrant
The Rectangular Coordinate System
,x y ,x y
,x y ,x y
x
y
The Rectangular Coordinate System 2,4,2,4,1,1,1,1,0,0 A
Graphs, Relations, and FunctionsDefn: A function is a relation where every x value has one and only one value of y assigned to it.
:range 6,5,4,3
3,2,1,4:domain
x y
1 3
2 5
-4 6
1 4
3 3
x y
4 2
-3 8
6 1
-1 9
5 6
x y
2 3
5 7
3 8
-2 -5
8 7
:range 9,8,6,2,1
6,5,4,1,3 :domain
:range 8,7,3,5
8,5,3,2,2:domain
Graphs, Relations, and FunctionsFunctions and Equations.
32 xy
x y
0 -3
5 7
-2 -7
4 5
3 3
x y
2 4
-2 4
-4 16
3 9
-3 9
x y
1 1
1 -1
4 2
4 -2
0 0
2xy 2yx
function function not a function
x
y
The Rectangular Coordinate System 32 xy
x y
0 -3
5 7
-2 -7
4 5
3 3
x
y
The Rectangular Coordinate System 2xy
x y
2 4
-2 4
-4 16
3 9
-3 9
x
y
The Rectangular Coordinate System 2yx
x y
1 1
1 -1
4 2
4 -2
0 0
x
y
The Rectangular Coordinate System
Graphs, Relations, and FunctionsFunction Notation
52 xxf
13 xxf 13 xxy
xfxyy
Shorthand for stating that an equation is a function.
13 xy
Function notation also defines the value of x that is to be use to calculate the corresponding value of y.
Defines the independent variable (usually x) and the dependent variable (usually y).
5323 f 13 f 1,3
Graphs, Relations, and FunctionsFunction Notation – Restricted Domains
24 xxfy
42 xxfy
0x
042 x
x
xfy4
04 2 x