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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 21 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 community health?

- Inequalities <, >, ≤, ≥

        “( “  →  <, >, o, open (not included)

        “[“  →  ≤, ≥, ∙, closedIf you want to learn more check out What is haymarket riot in 1886?

        “∞” → infinity, not a # always use “(“We also discuss several other topics like What are the ways to maximize objectivity?

- Additional Property

        If a<b ⇔ a+c < b+c

- Multiplication PropertyDon't forget about the age old question of What happen to the punic war?

        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

We also discuss several other topics like What are the ways to convert units?

1.7 VQ1

If you want to learn more check out What are the types of changes that affect cultural groups?

{ 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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