Asimtot tegak dari fungsi y=x2−8x+162x−2 adalah...

Pertanyaan

Asimtot tegak dari fungsi $begin mathsize 14px style straight y equals fraction numerator 2 straight x minus 2 over denominator square root of straight x squared minus 8 straight x plus 16 end root end fraction end style$ adalah ....

y =1
x = 2
y = 3
x = 4
x = 2

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

x = 4 adalah asimtot tegak dari fungsi $begin mathsize 14px style straight y equals fraction numerator 2 straight x minus 2 over denominator square root of straight x squared minus 8 straight x plus 16 end root end fraction end style$ .

Pembahasan

Perhatikan bahwa bentuk $begin mathsize 14px style fraction numerator 2 straight x minus 2 over denominator square root of straight x squared minus 8 straight x plus end root 16 end fraction end style$ memiliki penyebut = 0 jika x = 4.

Perhatikan bahwa

$begin mathsize 14px style limit as straight x rightwards arrow 4 to the power of plus of fraction numerator 2 straight x minus 2 over denominator square root of straight x squared minus 8 straight x plus 16 end root end fraction equals infinity limit as straight x rightwards arrow 4 to the power of minus of fraction numerator 2 straight x minus 2 over denominator square root of straight x squared minus 8 straight x plus 16 end root end fraction equals negative infinity end style$

Sehingga x = 4 adalah asimtot tegak dari fungsi $begin mathsize 14px style straight y equals fraction numerator 2 straight x minus 2 over denominator square root of straight x squared minus 8 straight x plus 16 end root end fraction end style$ .