{"id":567271,"date":"2026-07-23T09:31:23","date_gmt":"2026-07-23T02:31:23","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567271"},"modified":"2026-07-23T09:31:23","modified_gmt":"2026-07-23T02:31:23","slug":"ham-so-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/ham-so-la-gi\/","title":{"rendered":"H\u00e0m s\u1ed1 l\u00e0 g\u00ec? Kh\u00e1i ni\u1ec7m, t\u1eadp x\u00e1c \u0111\u1ecbnh v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1"},"content":{"rendered":"

H\u00e0m s\u1ed1 l\u00e0 m\u1ed9t quy t\u1eafc t\u01b0\u01a1ng \u1ee9ng, trong \u0111\u00f3 n\u1ebfu \u0111\u1ea1i l\u01b0\u1ee3ng y ph\u1ee5 thu\u1ed9c v\u00e0o \u0111\u1ea1i l\u01b0\u1ee3ng thay \u0111\u1ed5i x sao cho v\u1edbi m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a x ta lu\u00f4n x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c ch\u1ec9 m\u1ed9t gi\u00e1 tr\u1ecb t\u01b0\u01a1ng \u1ee9ng c\u1ee7a y, th\u00ec y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m s\u1ed1 c\u1ee7a x. Khi \u0111\u00f3 x g\u1ecdi l\u00e0 bi\u1ebfn s\u1ed1. \u0110\u00e2y l\u00e0 kh\u00e1i ni\u1ec7m n\u1ec1n t\u1ea3ng c\u1ee7a \u0110\u1ea1i s\u1ed1, theo b\u1ea1n t\u1eeb l\u1edbp 7 \u0111\u1ebfn l\u1edbp 12. B\u00e0i vi\u1ebft gi\u00fap b\u1ea1n hi\u1ec3u r\u00f5 h\u00e0m s\u1ed1 l\u00e0 g\u00ec<\/b>, c\u00e1ch cho h\u00e0m s\u1ed1, t\u1eadp x\u00e1c \u0111\u1ecbnh, \u0111\u1ed3 th\u1ecb, c\u00e1c h\u00e0m s\u1ed1 th\u01b0\u1eddng g\u1eb7p, nh\u1eefng l\u1ed7i hay m\u1eafc v\u00e0 b\u1ed9 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i t\u1eebng b\u01b0\u1edbc.<\/p>\n

H\u00e0m s\u1ed1 l\u00e0 g\u00ec?<\/b><\/h2>\n

H\u00e0m s\u1ed1 l\u00e0 quy t\u1eafc cho m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn x duy nh\u1ea5t m\u1ed9t gi\u00e1 tr\u1ecb y. N\u1ebfu \u0111\u1ea1i l\u01b0\u1ee3ng y ph\u1ee5 thu\u1ed9c v\u00e0o \u0111\u1ea1i l\u01b0\u1ee3ng thay \u0111\u1ed5i x sao cho v\u1edbi m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a x, ta lu\u00f4n x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c duy nh\u1ea5t m\u1ed9t gi\u00e1 tr\u1ecb t\u01b0\u01a1ng \u1ee9ng c\u1ee7a y, th\u00ec y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m s\u1ed1 c\u1ee7a x v\u00e0 x l\u00e0 bi\u1ebfn s\u1ed1.<\/p>\n

\u0110i\u1ec3m m\u1ea5u ch\u1ed1t c\u1ea7n nh\u1edb l\u00e0 m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a x ch\u1ec9 cho ra m\u1ed9t gi\u00e1 tr\u1ecb c\u1ee7a y. N\u1ebfu m\u1ed9t gi\u00e1 tr\u1ecb x l\u1ea1i \u1ee9ng v\u1edbi hai gi\u00e1 tr\u1ecb y kh\u00e1c nhau th\u00ec \u0111\u00f3 kh\u00f4ng ph\u1ea3i h\u00e0m s\u1ed1. H\u00e0m s\u1ed1 th\u01b0\u1eddng \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng y = f(x), trong \u0111\u00f3 f l\u00e0 k\u00fd hi\u1ec7u c\u1ee7a quy t\u1eafc t\u01b0\u01a1ng \u1ee9ng.<\/p>\n

\"ham-so-la-gi-2\"<\/p>\n

C\u00e1ch cho m\u1ed9t h\u00e0m s\u1ed1<\/b><\/h2>\n

M\u1ed9t h\u00e0m s\u1ed1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng nhi\u1ec1u c\u00e1ch kh\u00e1c nhau, gi\u00fap th\u1ec3 hi\u1ec7n m\u1ed1i quan h\u1ec7 gi\u1eefa bi\u1ebfn x v\u00e0 gi\u00e1 tr\u1ecb t\u01b0\u01a1ng \u1ee9ng c\u1ee7a y. Ba c\u00e1ch ph\u1ed5 bi\u1ebfn nh\u1ea5t l\u00e0 d\u00f9ng c\u00f4ng th\u1ee9c, b\u1ea3ng gi\u00e1 tr\u1ecb v\u00e0 \u0111\u1ed3 th\u1ecb.<\/p>\n

B\u1eb1ng c\u00f4ng th\u1ee9c: h\u00e0m s\u1ed1 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n th\u00f4ng qua m\u1ed9t bi\u1ec3u th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa x v\u00e0 y. V\u00ed d\u1ee5: y = 2x + 1, y = x\u00b2, y = 3\/x. \u0110\u00e2y l\u00e0 c\u00e1ch g\u1ecdn g\u00e0ng v\u00e0 th\u01b0\u1eddng g\u1eb7p nh\u1ea5t trong s\u00e1ch gi\u00e1o khoa.<\/p>\n

B\u1eb1ng b\u1ea3ng gi\u00e1 tr\u1ecb: ta li\u1ec7t k\u00ea c\u00e1c c\u1eb7p gi\u00e1 tr\u1ecb t\u01b0\u01a1ng \u1ee9ng c\u1ee7a x v\u00e0 y d\u01b0\u1edbi d\u1ea1ng b\u1ea3ng, t\u1eeb \u0111\u00f3 th\u1ec3 hi\u1ec7n r\u00f5 s\u1ef1 thay \u0111\u1ed5i c\u1ee7a h\u00e0m s\u1ed1 qua t\u1eebng m\u1ed1c c\u1ee5 th\u1ec3.<\/p>\n

B\u1eb1ng \u0111\u1ed3 th\u1ecb: ta bi\u1ec3u di\u1ec5n m\u1ed1i quan h\u1ec7 gi\u1eefa x v\u00e0 y tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9, trong \u0111\u00f3 m\u1ed7i \u0111i\u1ec3m tr\u00ean \u0111\u1ed3 th\u1ecb t\u01b0\u01a1ng \u1ee9ng v\u1edbi m\u1ed9t c\u1eb7p gi\u00e1 tr\u1ecb (x, y) c\u1ee7a h\u00e0m s\u1ed1.<\/p>\n

T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec<\/b><\/h2>\n

T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 y = f(x) l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn x \u0111\u1ec3 bi\u1ec3u th\u1ee9c f(x) c\u00f3 ngh\u0129a. N\u00f3i c\u00e1ch kh\u00e1c, \u0111\u00e2y l\u00e0 nh\u1eefng gi\u00e1 tr\u1ecb m\u00e0 t\u1ea1i \u0111\u00f3 h\u00e0m s\u1ed1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n v\u00e0 x\u00e1c \u0111\u1ecbnh.<\/p>\n

V\u00ed d\u1ee5: h\u00e0m s\u1ed1 y = 3\/x x\u00e1c \u0111\u1ecbnh v\u1edbi m\u1ecdi x kh\u00e1c 0 v\u00ec m\u1eabu s\u1ed1 kh\u00f4ng \u0111\u01b0\u1ee3c b\u1eb1ng 0. Trong khi \u0111\u00f3, h\u00e0m s\u1ed1 y = 2x + 1 x\u00e1c \u0111\u1ecbnh v\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c x.<\/p>\n

Vi\u1ec7c t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 b\u01b0\u1edbc quan tr\u1ecdng c\u1ea7n th\u1ef1c hi\u1ec7n tr\u01b0\u1edbc khi kh\u1ea3o s\u00e1t v\u00e0 ph\u00e2n t\u00edch c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a h\u00e0m s\u1ed1, gi\u00fap \u0111\u1ea3m b\u1ea3o c\u00e1c ph\u00e9p t\u00ednh v\u00e0 k\u1ebft lu\u1eadn \u0111\u01b0\u1ee3c ch\u00ednh x\u00e1c.<\/p>\n

C\u00e1c b\u01b0\u1edbc t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh<\/b><\/h3>\n

\u0110\u1ec3 t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh, b\u1ea1n x\u00e9t \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 bi\u1ec3u th\u1ee9c c\u00f3 ngh\u0129a: m\u1eabu s\u1ed1 ph\u1ea3i kh\u00e1c 0 (v\u1edbi ph\u00e2n th\u1ee9c), bi\u1ec3u th\u1ee9c d\u01b0\u1edbi d\u1ea5u c\u0103n b\u1eadc hai ph\u1ea3i l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0 (v\u1edbi c\u0103n th\u1ee9c). Sau \u0111\u00f3 b\u1ea1n gi\u1ea3i c\u00e1c \u0111i\u1ec1u ki\u1ec7n \u0111\u00f3 v\u00e0 l\u1ea5y ph\u1ea7n giao l\u1ea1i. V\u00ed d\u1ee5 v\u1edbi y = 1\/\u221a(x \u2212 1), \u0111i\u1ec1u ki\u1ec7n l\u00e0 x \u2212 1 > 0, t\u1ee9c x > 1; v\u1eady t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 D = (1; +\u221e).<\/p>\n

\"ham-so-la-gi-4\"<\/p>\n

\u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1<\/b><\/h2>\n

\u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f(x) l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m c\u00f3 t\u1ecda \u0111\u1ed9 (x; f(x)) tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy. M\u1ed7i \u0111i\u1ec3m tr\u00ean \u0111\u1ed3 th\u1ecb bi\u1ec3u di\u1ec5n m\u1ed1i quan h\u1ec7 t\u01b0\u01a1ng \u1ee9ng gi\u1eefa gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn x v\u00e0 gi\u00e1 tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y.<\/p>\n

Th\u00f4ng qua vi\u1ec7c quan s\u00e1t \u0111\u1ed3 th\u1ecb, b\u1ea1n c\u00f3 th\u1ec3 nh\u1eadn bi\u1ebft nhi\u1ec1u \u0111\u1eb7c \u0111i\u1ec3m quan tr\u1ecdng c\u1ee7a h\u00e0m s\u1ed1 nh\u01b0 s\u1ef1 bi\u1ebfn thi\u00ean (\u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn), c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1eb7c bi\u1ec7t, c\u0169ng nh\u01b0 h\u00ecnh d\u1ea1ng v\u00e0 quy lu\u1eadt thay \u0111\u1ed5i c\u1ee7a h\u00e0m s\u1ed1.<\/p>\n

Ngo\u00e0i ra, \u0111\u1ed3 th\u1ecb c\u00f2n gi\u00fap x\u00e1c \u0111\u1ecbnh m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t kh\u00e1c c\u1ee7a h\u00e0m s\u1ed1 nh\u01b0 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t v\u00e0 h\u1ed7 tr\u1ee3 qu\u00e1 tr\u00ecnh kh\u1ea3o s\u00e1t, ph\u00e2n t\u00edch h\u00e0m s\u1ed1 m\u1ed9t c\u00e1ch tr\u1ef1c quan h\u01a1n.<\/p>\n

M\u1ed9t s\u1ed1 h\u00e0m s\u1ed1 th\u01b0\u1eddng g\u1eb7p<\/b><\/h2>\n

C\u00e1c h\u00e0m s\u1ed1 l\u00e0 m\u1ed9t trong nh\u1eefng n\u1ed9i dung quan tr\u1ecdng trong to\u00e1n h\u1ecdc, gi\u00fap m\u00f4 t\u1ea3 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng v\u00e0 bi\u1ec3u di\u1ec5n s\u1ef1 thay \u0111\u1ed5i c\u1ee7a ch\u00fang. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 d\u1ea1ng h\u00e0m s\u1ed1 th\u01b0\u1eddng g\u1eb7p, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng ph\u1ed5 bi\u1ebfn trong qu\u00e1 tr\u00ecnh h\u1ecdc t\u1eadp v\u00e0 gi\u1ea3i b\u00e0i t\u1eadp.<\/p>\n\n\n\n\n\n\n\n
H\u00e0m s\u1ed1<\/b><\/td>\nD\u1ea1ng c\u00f4ng th\u1ee9c<\/b><\/td>\n\u0110\u1ed3 th\u1ecb<\/b><\/td>\n<\/tr>\n
H\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t<\/td>\ny = ax + b (a \u2260 0)<\/td>\n\u0110\u01b0\u1eddng th\u1eb3ng<\/td>\n<\/tr>\n
H\u00e0m s\u1ed1 b\u1eadc hai<\/td>\ny = ax\u00b2 + bx + c (a \u2260 0)<\/td>\n\u0110\u01b0\u1eddng parabol<\/td>\n<\/tr>\n
H\u00e0m s\u1ed1 h\u1eb1ng<\/td>\ny = b<\/td>\n\u0110\u01b0\u1eddng th\u1eb3ng song song tr\u1ee5c ho\u00e0nh<\/td>\n<\/tr>\n
H\u00e0m s\u1ed1 ph\u00e2n th\u1ee9c<\/td>\ny = (ax + b)\/(cx + d)<\/td>\n\u0110\u01b0\u1eddng hypebol<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"ham-so-la-gi-3\"<\/p>\n

H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn v\u00e0 ngh\u1ecbch bi\u1ebfn<\/b><\/h2>\n

Tr\u00ean m\u1ed9t kho\u1ea3ng x\u00e1c \u0111\u1ecbnh, h\u00e0m s\u1ed1 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u1ed3ng bi\u1ebfn (h\u00e0m t\u0103ng) n\u1ebfu khi gi\u00e1 tr\u1ecb c\u1ee7a x t\u0103ng th\u00ec gi\u00e1 tr\u1ecb t\u01b0\u01a1ng \u1ee9ng c\u1ee7a y c\u0169ng t\u0103ng theo. Ng\u01b0\u1ee3c l\u1ea1i, h\u00e0m s\u1ed1 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ngh\u1ecbch bi\u1ebfn (h\u00e0m gi\u1ea3m) n\u1ebfu khi x t\u0103ng th\u00ec y gi\u1ea3m.<\/p>\n

V\u00ed d\u1ee5, v\u1edbi h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t y = ax + b, n\u1ebfu a > 0 th\u00ec h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean t\u1eadp x\u00e1c \u0111\u1ecbnh; n\u1ebfu a < 0 th\u00ec h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean t\u1eadp x\u00e1c \u0111\u1ecbnh.<\/p>\n

Vi\u1ec7c x\u00e9t t\u00ednh \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn gi\u00fap b\u1ea1n hi\u1ec3u \u0111\u01b0\u1ee3c chi\u1ec1u thay \u0111\u1ed5i c\u1ee7a h\u00e0m s\u1ed1, t\u1eeb \u0111\u00f3 h\u1ed7 tr\u1ee3 qu\u00e1 tr\u00ecnh ph\u00e2n t\u00edch v\u00e0 kh\u1ea3o s\u00e1t c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a h\u00e0m s\u1ed1.<\/p>\n

Nh\u1eefng l\u1ed7i th\u01b0\u1eddng g\u1eb7p khi l\u00e0m b\u00e0i v\u1ec1 h\u00e0m s\u1ed1<\/b><\/h2>\n

Khi m\u1edbi h\u1ecdc, b\u1ea1n r\u1ea5t d\u1ec5 m\u1eafc m\u1ed9t v\u00e0i l\u1ed7i c\u01a1 b\u1ea3n khi\u1ebfn k\u1ebft qu\u1ea3 sai d\u00f9 c\u00e1ch l\u00e0m g\u1ea7n \u0111\u00fang. N\u1eafm tr\u01b0\u1edbc nh\u1eefng l\u1ed7i n\u00e0y gi\u00fap b\u1ea1n tr\u00e1nh m\u1ea5t \u0111i\u1ec3m \u0111\u00e1ng ti\u1ebfc trong b\u00e0i ki\u1ec3m tra.<\/p>\n

L\u1ed7i qu\u00ean \u0111i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh: nhi\u1ec1u b\u1ea1n gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh ho\u1eb7c t\u00ednh gi\u00e1 tr\u1ecb m\u00e0 qu\u00ean \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n m\u1eabu kh\u00e1c 0 hay bi\u1ec3u th\u1ee9c trong c\u0103n kh\u00f4ng \u00e2m, d\u1eabn t\u1edbi nh\u1eadn nghi\u1ec7m kh\u00f4ng h\u1ee3p l\u1ec7.<\/p>\n

L\u1ed7i nh\u1ea7m bi\u1ebfn v\u00e0 gi\u00e1 tr\u1ecb h\u00e0m s\u1ed1: khi t\u00ednh f(a), b\u1ea1n c\u1ea7n thay a v\u00e0o \u0111\u00fang v\u1ecb tr\u00ed c\u1ee7a x, kh\u00f4ng nh\u1ea7m v\u1edbi y. Ngo\u00e0i ra, c\u1ea7n ph\u00e2n bi\u1ec7t r\u00f5 \u0111i\u1ec3m (x; y) tr\u00ean \u0111\u1ed3 th\u1ecb v\u1edbi c\u1eb7p gi\u00e1 tr\u1ecb trong b\u1ea3ng.<\/p>\n

L\u1ed7i k\u1ebft lu\u1eadn \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn sai d\u1ea5u: v\u1edbi h\u00e0m b\u1eadc nh\u1ea5t, ch\u1ec9 c\u1ea7n x\u00e9t d\u1ea5u c\u1ee7a h\u1ec7 s\u1ed1 a; a d\u01b0\u01a1ng l\u00e0 \u0111\u1ed3ng bi\u1ebfn, a \u00e2m l\u00e0 ngh\u1ecbch bi\u1ebfn, \u0111\u1eebng \u0111\u1ea3o ng\u01b0\u1ee3c.<\/p>\n

B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i<\/b><\/h2>\n

B\u00e0i 1: T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = 2x + 1 t\u1ea1i x = 3. L\u1eddi gi\u1ea3i: thay x = 3 v\u00e0o c\u00f4ng th\u1ee9c, ta c\u00f3 y = 2\u00b73 + 1 = 6 + 1 = 7. V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 t\u1ea1i x = 3 l\u00e0 7.<\/p>\n

B\u00e0i 2: T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 y = 5\/(x \u2212 2). L\u1eddi gi\u1ea3i: bi\u1ec3u th\u1ee9c l\u00e0 ph\u00e2n th\u1ee9c n\u00ean c\u00f3 ngh\u0129a khi m\u1eabu kh\u00e1c 0, t\u1ee9c x \u2212 2 \u2260 0, suy ra x \u2260 2. T\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 D = \u211d \\ {2}, ngh\u0129a l\u00e0 m\u1ecdi s\u1ed1 th\u1ef1c tr\u1eeb x = 2.<\/p>\n

B\u00e0i 3: H\u00e0m s\u1ed1 y = \u22123x + 2 \u0111\u1ed3ng bi\u1ebfn hay ngh\u1ecbch bi\u1ebfn? L\u1eddi gi\u1ea3i: \u0111\u00e2y l\u00e0 h\u00e0m b\u1eadc nh\u1ea5t v\u1edbi h\u1ec7 s\u1ed1 a = \u22123. V\u00ec a = \u22123 < 0 n\u00ean h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean to\u00e0n t\u1eadp x\u00e1c \u0111\u1ecbnh.<\/p>\n

B\u00e0i 4: \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x \u0111i qua \u0111i\u1ec3m n\u00e0o trong hai \u0111i\u1ec3m (1; 2) v\u00e0 (1; 3)? L\u1eddi gi\u1ea3i: thay x = 1 v\u00e0o c\u00f4ng th\u1ee9c \u0111\u01b0\u1ee3c y = 2\u00b71 = 2, n\u00ean \u0111\u1ed3 th\u1ecb \u0111i qua \u0111i\u1ec3m (1; 2), kh\u00f4ng \u0111i qua (1; 3).<\/p>\n

B\u00e0i 5 (tr\u1eafc nghi\u1ec7m): H\u00e0m s\u1ed1 n\u00e0o sau \u0111\u00e2y l\u00e0 h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t? A. y = x\u00b2 B. y = 2x + 1 C. y = 3\/x D. y = x\u00b3. L\u1eddi gi\u1ea3i: h\u00e0m b\u1eadc nh\u1ea5t c\u00f3 d\u1ea1ng y = ax + b v\u1edbi a \u2260 0, n\u00ean \u0111\u00e1p \u00e1n l\u00e0 B.<\/p>\n

\"ham-so-la-gi-1\"<\/p>\n

C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 h\u00e0m s\u1ed1<\/b><\/h2>\n

H\u00e0m s\u1ed1 l\u00e0 g\u00ec?<\/b><\/h3>\n

H\u00e0m s\u1ed1 l\u00e0 quy t\u1eafc t\u01b0\u01a1ng \u1ee9ng trong \u0111\u00f3 m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a x x\u00e1c \u0111\u1ecbnh duy nh\u1ea5t m\u1ed9t gi\u00e1 tr\u1ecb c\u1ee7a y, th\u01b0\u1eddng vi\u1ebft l\u00e0 y = f(x).<\/p>\n

Bi\u1ebfn s\u1ed1 l\u00e0 g\u00ec?<\/b><\/h3>\n

Bi\u1ebfn s\u1ed1 l\u00e0 \u0111\u1ea1i l\u01b0\u1ee3ng x thay \u0111\u1ed5i m\u00e0 y ph\u1ee5 thu\u1ed9c v\u00e0o n\u00f3 trong quan h\u1ec7 h\u00e0m s\u1ed1 y = f(x).<\/p>\n

T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 g\u00ec?<\/b><\/h3>\n

T\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a x l\u00e0m cho bi\u1ec3u th\u1ee9c c\u1ee7a h\u00e0m s\u1ed1 c\u00f3 ngh\u0129a.<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 l\u00e0 g\u00ec?<\/b><\/h3>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 l\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m c\u00f3 t\u1ecda \u0111\u1ed9 (x; f(x)) \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy.<\/p>\n

H\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t c\u00f3 d\u1ea1ng g\u00ec?<\/b><\/h3>\n

H\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t c\u00f3 d\u1ea1ng y = ax + b v\u1edbi a kh\u00e1c 0, \u0111\u1ed3 th\u1ecb l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n

L\u00e0m sao bi\u1ebft m\u1ed9t quan h\u1ec7 c\u00f3 ph\u1ea3i h\u00e0m s\u1ed1 kh\u00f4ng?<\/b><\/h3>\n

N\u1ebfu m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a x ch\u1ec9 cho \u0111\u00fang m\u1ed9t gi\u00e1 tr\u1ecb c\u1ee7a y th\u00ec \u0111\u00f3 l\u00e0 h\u00e0m s\u1ed1; n\u1ebfu m\u1ed9t x cho t\u1eeb hai gi\u00e1 tr\u1ecb y tr\u1edf l\u00ean th\u00ec kh\u00f4ng ph\u1ea3i.<\/p>\n

K\u1ebft lu\u1eadn<\/b><\/h2>\n

T\u00f3m l\u1ea1i, h\u00e0m s\u1ed1 l\u00e0 quy t\u1eafc cho m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn x t\u01b0\u01a1ng \u1ee9ng duy nh\u1ea5t m\u1ed9t gi\u00e1 tr\u1ecb y, vi\u1ebft l\u00e0 y = f(x). N\u1eafm v\u1eefng kh\u00e1i ni\u1ec7m t\u1eadp x\u00e1c \u0111\u1ecbnh, \u0111\u1ed3 th\u1ecb v\u00e0 c\u00e1c h\u00e0m s\u1ed1 th\u01b0\u1eddng g\u1eb7p s\u1ebd gi\u00fap b\u1ea1n h\u1ecdc t\u1ed1t \u0111\u1ea1i s\u1ed1 v\u00e0 gi\u1ea3i t\u00edch. \u0110\u1ec3 h\u1ecdc th\u00eam, m\u1eddi b\u1ea1n tham kh\u1ea3o c\u00e1c b\u00e0i c\u00f4ng th\u1ee9c t\u00ednh qu\u00e3ng \u0111\u01b0\u1eddng<\/a>, m\u1ed9t n\u0103m \u00e1nh s\u00e1ng b\u1eb1ng bao nhi\u00eau km<\/a> v\u00e0 di\u1ec7n t\u00edch c\u00e1c t\u1ec9nh Vi\u1ec7t Nam<\/a> tr\u00ean chuy\u00ean m\u1ee5c tin t\u1ee9c c\u1ee7a Ho\u00e0ng H\u00e0 Mobile.<\/p>\n

Xem th\u00eam:<\/b><\/p>\n