, .. ( , ), . , , . , . , :
, , , Ox , , y = 1 (, , ), . , , .. (¥, +¥), 0 1. :
D (2) = 1; D (0) = 1; D () = 0; D (2) = 1; D (p) = 0.
= x2, , .
= 2, , (. 4).
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f (x) = sign x = ( . signum ) (. 5).
, .. (¥, +¥), : 1, 0 1.
, - , .
:
1) ;
2) ;
3) ;
4) ;
5) () ;
6) () .
, (, ) : (, ), ( , ); ( + , ), ³ 0; (, + b), b ³ 0, (k, ), k > 0, (, m), m >0.
.
y = f (x). : y = f (x); y = f ( x); y = f (x ); y = f (x) + b; y = f (kx); y = mf (x).
4-9 .
10, 11 , .
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y = f (x) (1)
[ , b ], ( ) [ ; d ].
[ ; d ] [ , b ], f () = , [ ; d ]
x = j (y) (2)
, , [ , d ], [ , b ], f () = . (2) (1), , [ , d ], = f (j (y)). , (2) (1), , , (1) (2).
(1) (2) . , [ , b ] [ , d ] , , (, b) (, d).
, .
. = f (x) , .
.
, = f (), [ , b ] ( £ £ d), = j (), [ , d ] (a £ x £ b), (. 6). , = f (), [ , b ] ( £ £ d), = (), [ , d ]( £ £ b). = j () , , = j () [, d ] (), [ , b ] (), .. . , 180 , y = f (x) (. 7).
.
, = .
. 8 (, ).
) )
. 8
8 ) .
8 ) .
. , .
1) y = 2 x 3; 2) y =
.
1) = 2 3 (¥, +¥), (¥, +¥), (!), , , .
: = .
, = . , y = 2 x 3.
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2) y = (¥, 0) (0, +¥), (!). (¥, 0) (0, +¥), , = . , y = . , y = .