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6.2-bo'lim : Logarifm funktsiyalari

23. \(g\left( x \right) = \ln \left( x \right) - 4\) grafigini chizing.

Yechim

Ushbu muammo uchun biz qilishimiz kerak bo'lgan yagona narsa - eslash Transformatsiyalar bir necha bobdan oldingi qism. \(f\left( x \right) = \ln \left( x \right)\) ning “asosiy” funksiyasidan foydalanib, ushbu qism uchun funksiya quyidagicha yozilishi mumkin:

\[g\left( x \right) = \ln \left( x \right) - 4 = f\left( x \right) - 4\]

Shuning uchun, bu qism uchun grafik faqat 4 ga pastga siljigan \(f\left( x \right)\) grafigi.

Ushbu funktsiyaning grafigi quyida ko'rsatilgan. Moviy chiziqli chiziq “tayanch” funksiyasi, \(f\left( x \right)\) va qizil qattiq chiziq bu qismning grafigi, \(g\left( x \right)\).

The graph of \(g\left( x \right) = \ln \left( x \right) - 4\). The blue dashed line is the “base” function \(f\left( x \right) = \ln \left( x \right)\) and the solid red line is \(g\left( x \right)\), which is exactly the same shape shifted down by 4. The two graphs have the same shape with the solid one always sitting 4 units below the dashed one.