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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.

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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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