Asosiy tarkibga o'tish

1.10-bo'lim : Umumiy grafiklar

3. Grafik kalkulyatordan foydalanmasdan \(g\left( x \right) = \sin \left( x \right) + 6\) grafigini chizing.

Yechim

Asosiy algebraik o'zgarishlarni eslang. Agar biz \(f\left( x \right)\) grafigini bilsak, \(f\left( x \right) + c\) grafigi oddiygina \(f\left( x \right)\) 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 \(f\left( x \right) = \sin \left( x \right)\), biz buni ko'rishimiz mumkin,

\[g\left( x \right) = \sin \left( x \right) + 6 = f\left( x \right) + 6\]

va shuning uchun bizdan eskiz qilishimiz so'ralgan grafik sinus funksiyasining 6 birlikka siljigan grafigidir.

Mana \(g\left( x \right) = \sin \left( x \right) + 6\) grafigi va esda tutingki, transformatsiyani ko'rishga yordam berish uchun biz \(f\left( x \right) = \sin \left( x \right)\) grafigida ham chizganmiz.

The graph of \(g\left( x \right) = \sin \left( x \right) + 6\), drawn as a solid red curve, along with the graph of \(f\left( x \right) = \sin \left( x \right)\), drawn as a dashed gray curve, for \( - 2\pi \le x \le 2\pi \).  The graph of \(f\left( x \right)\) oscillates between -1 and 1 while the graph of \(g\left( x \right)\) has the same shape but oscillates between 5 and 7, so it is the graph of \(f\left( x \right)\) shifted up 6 units.