,
2 , , .
, ( ). - , .
={(x,f(x)|xÎX}.
.
1. . f(-x)=f(x) "xÎD(f), =f(x) .
f(-x)= - f(x) "xÎD(f), =f(x) . , , .
2. . =f(x) , 1 2 (1<2) f(x1)<f(x2)
=f(x) , 1 2 (1>2) f(x1)>f(x2).
.
3. . =f(x) , >0, MÎR|"xÎ |f(x)|£M.
=f(x) , mÎR |"xÎ m£f(x). =f(x) , mÎR |"xÎ m³f(x).
4. . =f(x) , f(x+ - T)=f(x).
.
=f(x) =D(f) Y=E(f). , 1 2 f(x1) f(x2). Î Î| y=f(x). f-1: Ӯ. . .
.
t=h(x), [xÎD(h), T=E(h)] y=g(t), [tÎT=D(g), Y=E(g)] ( ) : Î y=g(h(x)). .
.
1. . y=xa, a=const, aÎR. D(f)=(0;+¥). aÎNÞD(f)=R.
2. . y=ax, a>0,a 1. D(f)=R/ E(f)=(0;+¥). a>1, , . Î(0;1), .
3. . y=logax, a>0, a 1. D(f)=(0;+¥), E(f)=R. a>1, , . Î(0;1), .
|
|
4. .
5. .
. = f (x) 0 ( →0) , { n} , ( n≠ 0) . :
(*)
→∞ ( 0 +∞ -∞). , (*) : { n}, 0, { f (n)} .
.
. f (x) . →0,
→0,
. 1. ( →0) ( →0).