Die grafiek van $f(x)=3^{-x}$ is hieronder geteken - NSC Mathematics - Question 5 - 2020 - Paper 1
Question 5
Die grafiek van $f(x)=3^{-x}$ is hieronder geteken. A is die $y$-afsnit van $f$. B is die snypunt van $f$ en die lyn $y=9$.
5.1 Skryf die koördinate van A neer.
5.2 ... show full transcript
Worked Solution & Example Answer:Die grafiek van $f(x)=3^{-x}$ is hieronder geteken - NSC Mathematics - Question 5 - 2020 - Paper 1
Step 1
Skryf die koördinate van A neer.
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Answer
A(0; 1)
Step 2
Bepaal die koördinate van B.
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Answer
Gegee 9=3−x, waarna ons kan eweredig veronderstel dat 3−x=9. Dit lei tot −x=2, dus x=−2. Dit gee ons die koördinate van B as B(-2; 9).
Step 3
Skryf die definisieverzameling van $f^{-1}$ neer.
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Die definisieverzameling van f−1 is xe(0;extofx>0).
Step 4
Beskryf die translasie van f na $h(x)= rac{27}{3^{-x}}$.
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h(x) is die translasie van f wat 3 eenhede na die regterkant verschuif (f verskuif 3 eenhede na die regterkant).
Step 5
Bepaal die waardes van $x$ waarvoor $h(x) < 1$.
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Answer
Oorweeg die ongelykheid rac{27}{3^{-x}} < 1. Dit lei tot 27<3−x. Gegee 3−x>27 moet ons −x>3, hoedanig x<−3.
