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基本初等函数
2022-07-27 21:52:00 【MR_普罗米修斯】
【 1、常函数 】
y = C , C 为 常 数 y=C,C为常数 y=C,C为常数
【 2、幂函数 】
y = x a , a 为 常 数 y=x^a,a 为常数 y=xa,a为常数
其中,x叫做底数,a叫做指数。
【 3、指数函数 】
y = a x , a > 0 且 a ≠ 1 y=a^x,a>0且a≠1 y=ax,a>0且a=1
其中,a叫做底数,x叫做指数。
a m ⋅ a n = a m + n a^m·a^n=a^{m+n} am⋅an=am+n
a m a n = a m − n \frac{a^m}{a^n}=a^{m-n} anam=am−n
( a m ) n = a m n (a^m)^n=a^{mn} (am)n=amn
【 4、对数函数 】
y = l o g a x , a > 0 且 a ≠ 1 且 x > 0 y =log_ax,a>0且a≠1且x>0 y=logax,a>0且a=1且x>0
其中,a叫做底数,x称为真数。
l o g a n b m = m n l o g a b , a > 0 且 a ≠ 1 且 b > 0 log_{a^n}b^m=\frac{m}{n}log_ab,a>0且a≠1且b>0 loganbm=nmlogab,a>0且a=1且b>0
l o g a b = 1 l o g b a , a > 0 且 a ≠ 1 且 b > 0 且 b ≠ 1 log_ab=\frac{1}{log_ba},a>0且a≠1且b>0且b≠1 logab=logba1,a>0且a=1且b>0且b=1
【 5、三角函数和反三角函数 】
y = A s i n ( w x + φ ) y=Asin(wx+φ) y=Asin(wx+φ)
类似的还有cos、tan、arcsin、arctan等。
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