Asosiy tarkibga o'tish

6.1-bo'lim : Eksponensial funksiyalar

4. \(f\left( x \right) = {{\bf{e}}^{ - x}}\) 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:

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

Shuning uchun, bu qism uchun grafik faqat \(y\) o'qi haqida aks ettirilgan \(f\left( x \right)\) 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 \(g\left( x \right) = {{\bf{e}}^{ - x}}\). 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 the graph of \(f\left( x \right)\) reflected about the y-axis. The dashed graph increases to the right while the solid graph decreases to the right, and the two cross at \(\left( {0,1} \right)\).