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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

Hersiening

  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

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
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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