Asosiy tarkibga o'tish

6.1-bo'lim : Eksponensial funksiyalar

5. \(f\left( x \right) = {{\bf{e}}^{x - 3}} + 6\) grafigini chizing.

Yechim

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

\[f\left( x \right) = {{\bf{e}}^{x - 3}} + 6 = f\left( {x - 3} \right) + 6\]

Shuning uchun, bu qismning grafigi faqat \(f\left( x \right)\) ning o'ngga 3 ga va 6 ga yuqoriga siljigan grafigidir.

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 \(g\left( x \right) = {{\bf{e}}^{x - 3}} + 6\). The blue dashed line is the “base” function \(f\left( x \right) = {{\bf{e}}^x}\) and the solid red line is \(g\left( x \right)\), which is exactly the same shape shifted right by 3 and up by 6. The solid graph flattens out along the horizontal line \(y = 6\) on the left instead of along the x-axis.