CommonGraphs - 4-masala yechimi | MathModel.uz

1.10-bo'lim : Umumiy grafiklar

4. Grafik kalkulyatordan foydalanmasdan $f\left( x \right) = \ln \left( x \right) - 5$ grafigini chizing.

Yechim

Asosiy algebraik o'zgarishlarni eslang. Agar biz $g\left( x \right)$ grafigini bilsak, $g\left( x \right) + c$ grafigi oddiygina $g\left( x \right)$ ning grafigi, agar $c < 0$ bo'lsa, $c$ birliklari bilan pastga siljiydi yoki $c > 0$ bo'lsa, $c$ birliklari bilan yuqoriga siljiydi.

Shunday qilib, bizning holatlarimizda $g\left( x \right) = \ln \left( x \right)$, biz buni ko'rishimiz mumkin,

\[f\left( x \right) = \ln \left( x \right) - 5 = g\left( x \right) - 5\]

va shuning uchun bizdan eskiz qilishimiz so'ralayotgan grafik tabiiy logarifm funksiyasining 5 birlik pastga siljigan grafigi.

Mana $f\left( x \right) = \ln \left( x \right) - 5$ grafigi va esda tutingki, transformatsiyani ko'rishga yordam berish uchun biz $g\left( x \right) = \ln \left( x \right)$ grafigida ham chizganmiz.

$The graph of $f\left( x \right) = \ln \left( x \right) - 5$, drawn as a solid red curve, along with the graph of $g\left( x \right) = \ln \left( x \right)$, drawn as a dashed gray curve, for $x$ between 0 and 5. Both curves have a vertical asymptote at $x = 0$ and increase slowly as $x$ increases. The graph of $g\left( x \right)$ crosses the $x$-axis at (1,0) while the graph of $f\left( x \right)$ passes through (1,-5), so it is the graph of $g\left( x \right)$ shifted down 5 units.$