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Ons gaan albei notasies in hierdie boek gebruik.

Indien f ( n ) = n 2 - 6 n + 9 , vind f ( k - 1 ) in terme van k .

  1. f ( n ) = n 2 - 6 n + 9 f ( k - 1 ) = ( k - 1 ) 2 - 6 ( k - 1 ) + 9
  2. = k 2 - 2 k + 1 - 6 k + 6 + 9 = k 2 - 8 k + 16

    Ons het nou die funksie vereenvoudig interme van k .

As f ( x ) = x 2 - 4 , bereken b as f ( b ) = 45 .

  1. f ( b ) = b 2 - 4 maar f ( b ) = 45
  2. b 2 - 4 = 45 b 2 - 49 = 0 b = + 7 or - 7


  1. Raai watter funksie, in die vorm y = ... , word voorgestel deur die waardes in die tabel.
    x 1 2 3 40 50 600 700 800 900 1000
    y 1 2 3 40 50 600 700 800 900 1000
  2. Raai watter funksie, in die vorm y = ... , word voorgestel deur die waardes in die tabel.
    x 1 2 3 40 50 600 700 800 900 1000
    y 2 4 6 80 100 1200 1400 1600 1800 2000
  3. Raai watter funksie, in die vorm y = ... , word voorgestel deur die waardes in die tabel.
    x 1 2 3 40 50 600 700 800 900 1000
    y 10 20 30 400 500 6000 7000 8000 9000 10000
  4. Stip die volgende punte (1;2), (2;4), (3;6), (4;8), (5;10) op 'n Cartesiese vlak. Verbind die punte. Kry jy 'n reguitlyn?
  5. Indien f ( x ) = x + x 2 , skryf neer:
    1. f ( t )
    2. f ( a )
    3. f ( 1 )
    4. f ( 3 )
  6. Indien g ( x ) = x and f ( x ) = 2 x , skryf neer:
    1. f ( t ) + g ( t )
    2. f ( a ) - g ( a )
    3. f ( 1 ) + g ( 2 )
    4. f ( 3 ) + g ( s )
  7. Jy staan langs 'n reguit snelweg, 'n motor ry by jou verby en beweeg 10m elke sekonde. Voltooi die tabel hieronder, deur in te vul hoe ver die motor van jou af wegbeweeg het na 5,10 en na 20 sekondes.
    Tyd (s) 0 1 2 5 10 20
    Afstand (m) 0 10 20
    Gebruik die waardes in die tabel en teken 'n grafiek met die afstand op die y -as en tyd op die x -as.

Kenmerke van alle funksies

Daar is baie verskillende kenmerke van grafieke wat die eienskappe van ’n spesifieke funksie se grafiek beskryf. Hierdie eienskappe gaan behandel word in hierdie hoofstuk en is die volgende:

  1. Afhanklike en onafhanklike veranderlikes
  2. Definisie- en waardeversameling
  3. Afsnitte met die asse
  4. Draaipunte
  5. Asimptote
  6. Lyne/asse van simmetrie
  7. Intervalle waar die funksie toeneem/afneem
  8. Kontinue gedrag van funksies

Sommige van die woorde mag onbekend wees vir jou, maar elke begrip sal duidelik beskryf word. Voorbeelde van sommige van die eienskappe word gewys in [link] .

(a) Voorbeeld van grafiek wat die eienskappe van 'n funksie illustreer (b) Voorbeeld van grafiek wat die asimptote van ’n funksie illustreer. Die asimptote is die stippellyne.

Afhanklike en onafhanklike veranderlikes

Tot dusver het al die grafieke wat ons gesien het twee veranderlikes, ’n x -waarde en ’n y -waarde. Die y -waarde word gewoonlik bepaal deur een of ander verband gebaseer op ’n gegewe of gekose x -waarde. Ons noem die x -waarde die onafhanklike veranderlike, omdat die waarde vrylik gekies kan word. Die berekende y -waarde is bekend as die afhanklike veranderlike, omdat die waarde afhanklik is van die gekose x -waarde.

Definisieversameling en waardeversameling

Die definisieversameling (ook bekend as die gebied) van ’n verband is die stel x waardes waarvoor daar te minste een y waarde bestaan. Die waardeversameling (ook bekend as die terrein) is die stel y waardes wat bepaal kan word deur te minste een x waarde. Anders gestel, die definisieversameling is alle moontlike insette en die waardeversameling is die alle moontlike uitsette.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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