Gegee funksies $f$ en $k$ wat onderskeidelik deur $f(x) = -x + 4$ en $k(x) =
oot{2}{-x^2}$ gedefinieer word - NSC Technical Mathematics - Question 4 - 2020 - Paper 1
Question 4
Gegee funksies $f$ en $k$ wat onderskeidelik deur $f(x) = -x + 4$ en $k(x) =
oot{2}{-x^2}$ gedefinieer word. Funksies $f$ en $k$ het dieselfde $y$-asfins.
4.1.1 Sk... show full transcript
Worked Solution & Example Answer:Gegee funksies $f$ en $k$ wat onderskeidelik deur $f(x) = -x + 4$ en $k(x) =
oot{2}{-x^2}$ gedefinieer word - NSC Technical Mathematics - Question 4 - 2020 - Paper 1
Step 1
4.1.1 Skryf die lengte van die radius van $k$ neer.
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Answer
Die radius van die funksie k(x)=oot2−x2 is 4.5 eenhede.
Step 2
4.1.2 Skets die grafieke van $f$ en $k$ op dieselfde assestelsel.
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Die grafiek van f(x)=−x+4 is 'n regshandige lyn wat die y-as by 4 sny en die x-as by 4. Die grafiek van k(x) is 'n halfsirkel gesentreer op die y-as, met die hoogste punt op 4 en die byskrif (asymptote) van k is y=0.
Step 3
4.1.3 Gee die definisiewisameling (gebied) van $k$.
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Die definisiewysameling van k is xextindieinterval[−4.5,4.5].
Step 4
4.2 Skets die grafiek van funksie $p$.
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Die grafiek van p(x) = - rac{4}{x} + q het 'n vertikale asímpoot by x=0 en 'n horisontale asímpoot wat bepaal kan word deur die limiet as xoextoneindig.
Step 5
4.3.1(a) Skryf neer die koördinate van $T$.
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Die koördinate van T is (0;16).
Step 6
4.3.1(b) Skryf neer die koördinate van $P$.
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Die koördinate van P is (−4;0).
Step 7
4.3.2 Bepaal die numeriese waarde(s) van $a$ en $b$.
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Die waardes van a en b kan gevind word deur die oplossing van die gelykstelling g(x)=a(x−x1)(x−x2).
Step 8
4.3.3 Bepaal die $y$-koördinaat van $R$.
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Die y-koördinaat van R kan bepaal word deur die waarde van g(x)∣(x=R)∣.
Step 9
4.3.4 Toon dat $h(x) = 2^{x + 8}$.
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Om te toon dat h(x)=2x+8 kan ons die waarde van h substitueer en herorganiseer.
Step 10
4.3.5 Skryf neer die waardeverzameling (terrein) van $h$.
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Die waardeverzameling van h is y>8.
Step 11
4.3.6 Bepaal die lengte van $VW$.
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Die lengte van VW kan bereken word aan die hand van die formules en die koördinate van die punte.
