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Samenvatting Algebraïsche functies
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Algebraïsche functies, horende bij wiskunde
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WiskundeSemester 1
2: Algebraïsche functies
Concepten
Algemeen: afhankelijke variabele= functie v/d onafhankelijke variabelen (n, T, P)
V(afhankelijke variabele)= n.R.T / P.
Functies van 1 variabele. Y is bepaald door x volgens het gegeven functievoorschrift. Bv. y=2x²+3x
Grafische voorstelling van functies
Cartesisch(=rechthoekig) coördinaatstelstel/systeem
Oorsprong O(0,0) & 2 loodrechte assen(met bep.zin)
Ieder punt i/h vlak is bepaald door een koppel coördinaten (x,y)
x: abscis(onafhankelijk) & y: ordinaat(afhankelijk)
Factorisatie = vereenvoudiging en / of verduidelijking van algebraïsche uitdrukkingen
Vb: 3xy + 6x² = (3x) . (y + 2x) = 3x(y+2x)
Expansie(enkel termen)= inverse manipulatie van factorisatie
Vb.:
-kwadraat van som
-kwadraat van verschil
-verschil van kwadraten
,Wiskunde
Semester 1
Vb.: 2.7
Inverse functies
Als y=f(x), dan x=f-1(y). ! f-1 ≠ 1/f
-Vb. : 2.9
-Vb.:
-Vb.: 2.12
, Wiskunde
Semester 1
Veeltermen(polynomen)
Polynoom graad n met constante coëfficiënten a0, a1, …, an:
Vb.: 2.13
Graad n = 1: lineaire functie(rechte)
Graad n = 2: kwadratische functie (parabool)
Vb.: 2.16
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