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TCU / Math / MATH 104 / What is stated in multiplication property?

What is stated in multiplication property?

What is stated in multiplication property?

Description

School: Texas Christian University
Department: Math
Course: algebra
Term: Spring 2019
Tags: Math and Algebra
Cost: 25
Name: Algebra week 2
Description: Covers section 1.7 and 2.1
Uploaded: 02/11/2019
2 Pages 65 Views 1 Unlocks
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"}ul.lst-kix_3p07ztch58cd-0{list-style-type:none}ul.lst-kix_3p07ztch58cd-1{list-style-type:none}ol.lst-kix_79bbyi6voafv-7{list-style-type:none}ol.lst-kix_79bbyi6voafv-8{list-style-type:none}ul.lst-kix_e3qza3jtdew8-2{list-style-type:none}ol.lst-kix_79bbyi6voafv-5{list-style-type:none}ul.lst-kix_e3qza3jtdew8-3{list-style-type:none}ol.lst-kix_79bbyi6voafv-6{list-style-type:none}ul.lst-kix_e3qza3jtdew8-0{list-style-type:none}.lst-kix_hy5hidfmj77p-3 > li:before{content:"● "}ol.lst-kix_79bbyi6voafv-3{list-style-type:none}ul.lst-kix_e3qza3jtdew8-1{list-style-type:none}ol.lst-kix_79bbyi6voafv-4{list-style-type:none}ol.lst-kix_79bbyi6voafv-8.start{counter-reset:lst-ctn-kix_79bbyi6voafv-8 0}ul.lst-kix_e3qza3jtdew8-6{list-style-type:none}.lst-kix_hy5hidfmj77p-2 > li:before{content:"■ "}ul.lst-kix_3p07ztch58cd-8{list-style-type:none}ul.lst-kix_e3qza3jtdew8-7{list-style-type:none}ul.lst-kix_e3qza3jtdew8-4{list-style-type:none}ul.lst-kix_3p07ztch58cd-6{list-style-type:none}ul.lst-kix_e3qza3jtdew8-5{list-style-type:none}ul.lst-kix_3p07ztch58cd-7{list-style-type:none}.lst-kix_hy5hidfmj77p-0 > li:before{content:"● "}ul.lst-kix_3p07ztch58cd-4{list-style-type:none}.lst-kix_3fwwteakwuuk-1 > li:before{content:"◆ "}.lst-kix_79bbyi6voafv-2 > li{counter-increment:lst-ctn-kix_79bbyi6voafv-2}ul.lst-kix_3p07ztch58cd-5{list-style-type:none}ul.lst-kix_e3qza3jtdew8-8{list-style-type:none}.lst-kix_hy5hidfmj77p-1 > li:before{content:"○ "}ul.lst-kix_3p07ztch58cd-2{list-style-type:none}.lst-kix_3fwwteakwuuk-0 > li:before{content:"➔ "}ul.lst-kix_3p07ztch58cd-3{list-style-type:none}ul.lst-kix_3fwwteakwuuk-2{list-style-type:none}ul.lst-kix_3fwwteakwuuk-1{list-style-type:none}ul.lst-kix_3fwwteakwuuk-0{list-style-type:none}ul.lst-kix_3fwwteakwuuk-6{list-style-type:none}ul.lst-kix_3fwwteakwuuk-5{list-style-type:none}ul.lst-kix_3fwwteakwuuk-4{list-style-type:none}ul.lst-kix_3fwwteakwuuk-3{list-style-type:none}ol.lst-kix_79bbyi6voafv-1{list-style-type:none}ol.lst-kix_79bbyi6voafv-2{list-style-type:none}ul.lst-kix_3fwwteakwuuk-8{list-style-type:none}ol.lst-kix_79bbyi6voafv-5.start{counter-reset:lst-ctn-kix_79bbyi6voafv-5 0}ul.lst-kix_3fwwteakwuuk-7{list-style-type:none}ol.lst-kix_79bbyi6voafv-0{list-style-type:none}ol.lst-kix_79bbyi6voafv-7.start{counter-reset:lst-ctn-kix_79bbyi6voafv-7 0}.lst-kix_79bbyi6voafv-3 > li{counter-increment:lst-ctn-kix_79bbyi6voafv-3}.lst-kix_tc441ovgrgd0-8 > li:before{content:"■ "}.lst-kix_hy5hidfmj77p-6 > li:before{content:"● "}.lst-kix_tc441ovgrgd0-3 > li:before{content:"● "}.lst-kix_tc441ovgrgd0-5 > li:before{content:"■ "}.lst-kix_kjv7guuq4ye9-4 > li:before{content:"- "}.lst-kix_kjv7guuq4ye9-6 > li:before{content:"- "}ol.lst-kix_79bbyi6voafv-6.start{counter-reset:lst-ctn-kix_79bbyi6voafv-6 0}.lst-kix_hy5hidfmj77p-7 > li:before{content:"○ "}.lst-kix_tc441ovgrgd0-0 > li:before{content:"● "}.lst-kix_tc441ovgrgd0-4 > li:before{content:"○ "}.lst-kix_kjv7guuq4ye9-3 > li:before{content:"- "}.lst-kix_kjv7guuq4ye9-7 > li:before{content:"- "}.lst-kix_tc441ovgrgd0-7 > li:before{content:"○ "}.lst-kix_hy5hidfmj77p-8 > li:before{content:"■ "}.lst-kix_tc441ovgrgd0-6 > li:before{content:"● "}.lst-kix_kjv7guuq4ye9-5 > li:before{content:"- "}.lst-kix_tc441ovgrgd0-1 > li:before{content:"○ "}.lst-kix_kjv7guuq4ye9-0 > li:before{content:"- "}.lst-kix_kjv7guuq4ye9-2 > li:before{content:"- "}ol.lst-kix_79bbyi6voafv-0.start{counter-reset:lst-ctn-kix_79bbyi6voafv-0 0}.lst-kix_tc441ovgrgd0-2 > li:before{content:"■ "}.lst-kix_kjv7guuq4ye9-1 > li:before{content:"- "}

Linear Inequalities/ Absolute Value inequalities

  • Use interval notation
  • Find intersections and unions of intervals
  • Solve linear inequalities
  • Recognize inequalities with no solution or all real numbers as solutions
  • Solve compound inequalities
  • Solve absolute value inequalities

We also discuss several other topics like What is population health?
We also discuss several other topics like What is haymarket riot in 1886?

- Inequalities <, >, ≤, ≥If you want to learn more check out What is emile durkheim famous for?

        “( “  →  <, >, o, open (not included)Don't forget about the age old question of Who is philip v of macedon?

        “[“  →  ≤, ≥, ∙, closed

        “∞” → infinity, not a # always use “(“Don't forget about the age old question of What is solvent?

We also discuss several other topics like What are the types of changes that affect cultural groups?

- Additional Property

        If a<b ⇔ a+c < b+c

- Multiplication Property

        If a<b ⇔ ac < bc

- If multiplied, divide or change to negative flip inequalities

- Absolute value

  1. |u| < c ⇒ -c < u < c
  2. |u| > c ⇒ u < -c  or u>c

1.7 VQ1

{ x| -6 ≤ x < 3 }                                                 [ -6,3 )

1.7.1

{ x| -7 < x ≤  -4 }                                                (-7, -4 ]

1.7.11

{ x| x < 1}                                                           (-∞, 1 )

1.7 VQ 2

( -9, 7) ∩ [ -6,8 ]                                                                                      [ -6,7 )

1.7.21

2x+4 < 10

     -4    -4

<

   X < 3                  

(-∞, 3 )

1.7.31 Flip inequalities

x ≤    

     X ≥ -7

    [ -7,∞ )

1.7.35

4 (x+1) + 2 ≥ 3x + 12  

4x + 4 + 2 ≥ 3x + 12

4x + 6 ≥ 3x + 12

-3x            -3x

x + 6 ≥ + 12

     -6           -6

  x ≥ 6

 [ 6,∞ )

1.7.55

-7  < 2x -1 ≤ 5

+1            +1    +1

< ≤  

-3 < x ≤  3 

  ( -3, 3 ]

1.7.61

-5  ≤  x +3  ≤ 5

+3           +3

-8  ≤  x  ≤ 2

   [ -8, 2 ]

1.7.73

| 2x-2 | > 6

2x -2 < - 6 or 2x 2 > 6

      +2      +2           +2   +2

<    > 

   x < -2             x > 4

( -∞, -2 ) ∪ ( 4, ∞ )

1.7.83 flip it

| 7-x | <

| 7-x | > 5

7-x < 5  or  7-x > 5

-7       -7       -7        -7

<   > 

   x > 12              x < 2

( -∞, 2 ) ∪ ( 12, ∞ )

2.1

Basic of functions and their Graphs

  • Find the domain and range of a relation
  • Determine function
  • Determine whether an equation represents a function
  • Evaluate function
  • Graph function by plotting points
  • Use vertical line test to identify functions
  • Obtain information about function from its graph.
  • Identify domain and range
  • Identify intercepts

- Relation: ordered pairs (x,y)

- Domain: x-value/ x-axis

- Range: y-value/y-axis

-Function - a relation in which each member of the domain corresponds to exactly one member of the range

           CAN NOT REPEAT!!!

-Function Notation: ƒ(x) = y

-Vertical line test - if any vertical line intersects a graph in more than one point the graph does not define y as a function of x.

2.1.3 Determine function  

{ (2,4), (2,9), (4,4), (4,9)}

D: {2,4}

R: {4,9}     No! Not a function

2.1.29

ƒ(x) =  + 8x + 1                               ƒ(x+4) =  + 8 (x+4) + 1

ƒ(-5) =  + 8(-5) + 1                                  =  + 8x + 16 + 8 (x+4) + 1

        = 25 - 40 + 1                                          =  + 8x + 16 + 8x + 32 + 1

        = -15 + 1                                                = + 16 x + 49

        = -14  

ƒ(-x) =  + 8(-x) + 1                  = (-1)(-1) = 1

        =   + 8x + 1                           = (-1x-1)(-1) =  -1

2.1.33

ƒ(x) =  +1                     ƒ(63) =  + 1

ƒ(-1) = +1                        =  + 1

       = +1                                      = 8 + 1 = 9

      = 0 + 1

       = 1

ƒ(x-1) =  +1  

          =  +1

          =  +1    

2.1.39

ƒ(x) = x

g(x) = x-4

g(x) is shifted down 4 units

2.1.59 function

Not a function:

2.1.61

Function

D: (-∞, ∞ )        x-intercept: 0

R: (-∞, ∞ )       y-intercept: 0

2.1.77

D: (-∞, ∞ )        

R: (-∞, 1 ]  

x-intercept: -1,1                                                        

y-intercept: 1

ƒ(-2) = -3

ƒ(2) = -3

2.1.81

D: (-4, 3 ]        

R: [-9, 7 ]  

x-intercept: -3,2                                                        

y-intercept: -9

2.1.89

D: (-∞, ∞ )        

R: (0, ∞ )  

x-intercept: None                                                      

y-intercept: 1

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