{"id":570825,"date":"2026-07-27T15:03:48","date_gmt":"2026-07-27T08:03:48","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=570825"},"modified":"2026-07-27T15:03:48","modified_gmt":"2026-07-27T08:03:48","slug":"duong-tiem-can-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/duong-tiem-can-la-gi\/","title":{"rendered":"\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn l\u00e0 g\u00ec? C\u00e1ch t\u00ecm ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0 ti\u1ec7m c\u1eadn ngang"},"content":{"rendered":"<p><strong>\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng m\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m tr\u00ean \u0111\u1ed3 th\u1ecb \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3 d\u1ea7n ti\u1ebfn v\u1ec1 0 khi \u0111i\u1ec3m ch\u1ea1y ra xa v\u00f4 t\u1eadn.<\/strong> Ba lo\u1ea1i th\u01b0\u1eddng g\u1eb7p l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng, ti\u1ec7m c\u1eadn ngang v\u00e0 ti\u1ec7m c\u1eadn xi\u00ean. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c n\u1ec1n c\u1ee7a Gi\u1ea3i t\u00edch l\u1edbp 12, ph\u1ee5c v\u1ee5 tr\u1ef1c ti\u1ebfp cho vi\u1ec7c kh\u1ea3o s\u00e1t v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. N\u1ebfu b\u1ea1n hay l\u00fang t\u00fang khi t\u00ecm ti\u1ec7m c\u1eadn c\u1ee7a h\u00e0m ph\u00e2n th\u1ee9c ho\u1eb7c nh\u1ea7m l\u1eabn gi\u1eefa c\u00e1c lo\u1ea1i, ph\u1ea7n tr\u00ecnh b\u00e0y d\u01b0\u1edbi \u0111\u00e2y s\u1ebd gi\u00fap b\u1ea1n n\u1eafm ch\u1eafc \u0111\u1ecbnh ngh\u0129a, c\u00e1ch t\u00ecm v\u00e0 luy\u1ec7n t\u1eadp qua v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft.<\/p>\n<h2>\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn l\u00e0 g\u00ec?<\/h2>\n<p>\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng m\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00e0ng l\u00fac c\u00e0ng ti\u1ebfn s\u00e1t khi bi\u1ebfn s\u1ed1 ho\u1eb7c gi\u00e1 tr\u1ecb h\u00e0m s\u1ed1 ti\u1ebfn ra v\u00f4 c\u1ef1c, nh\u01b0ng th\u01b0\u1eddng kh\u00f4ng c\u1eaft ho\u1eb7c ch\u1ec9 c\u1eaft t\u1ea1i h\u1eefu h\u1ea1n \u0111i\u1ec3m. Vi\u1ec7c x\u00e1c \u0111\u1ecbnh ti\u1ec7m c\u1eadn gi\u00fap ta h\u00ecnh dung \u0111\u01b0\u1ee3c &#8220;d\u00e1ng \u0111i\u1ec7u&#8221; c\u1ee7a \u0111\u1ed3 th\u1ecb \u1edf v\u00f4 c\u1ef1c, t\u1eeb \u0111\u00f3 kh\u1ea3o s\u00e1t v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb ch\u00ednh x\u00e1c h\u01a1n. V\u1edbi ch\u01b0\u01a1ng tr\u00ecnh ph\u1ed5 th\u00f4ng, ti\u1ec7m c\u1eadn xu\u1ea5t hi\u1ec7n nhi\u1ec1u nh\u1ea5t \u1edf c\u00e1c h\u00e0m ph\u00e2n th\u1ee9c h\u1eefu t\u1ec9 nh\u01b0 y = (ax + b)\/(cx + d).<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-570826\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-1.jpg\" alt=\"duong-tiem-can-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>Tr\u01b0\u1edbc khi t\u00ecm ti\u1ec7m c\u1eadn, b\u1ea1n n\u00ean n\u1eafm v\u1eefng kh\u00e1i ni\u1ec7m <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/ham-so-la-gi\/\">h\u00e0m s\u1ed1 l\u00e0 g\u00ec<\/a> c\u00f9ng c\u00e1ch x\u00e1c \u0111\u1ecbnh t\u1eadp x\u00e1c \u0111\u1ecbnh, v\u00ec \u0111\u00e2y l\u00e0 b\u01b0\u1edbc \u0111\u1ea7u ti\u00ean \u0111\u1ec3 ph\u00e1t hi\u1ec7n c\u00e1c \u0111i\u1ec3m nghi ng\u1edd c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng.<\/p>\n<h2>Ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 g\u00ec v\u00e0 c\u00e1ch t\u00ecm<\/h2>\n<p>\u0110\u01b0\u1eddng th\u1eb3ng x = a \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 <strong>ti\u1ec7m c\u1eadn \u0111\u1ee9ng<\/strong> c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f(x) n\u1ebfu \u00edt nh\u1ea5t m\u1ed9t trong c\u00e1c gi\u1edbi h\u1ea1n m\u1ed9t b\u00ean c\u1ee7a f(x) khi x ti\u1ebfn t\u1edbi a l\u00e0 v\u00f4 c\u1ef1c:<\/p>\n<p><strong>lim f(x) = +\u221e ho\u1eb7c \u2212\u221e khi x \u2192 a\u207a ho\u1eb7c x \u2192 a\u207b<\/strong><\/p>\n<p>Ti\u1ec7m c\u1eadn \u0111\u1ee9ng th\u01b0\u1eddng xu\u1ea5t hi\u1ec7n t\u1ea1i nh\u1eefng \u0111i\u1ec3m l\u00e0m m\u1eabu s\u1ed1 b\u1eb1ng 0 m\u00e0 t\u1eed s\u1ed1 kh\u00e1c 0. C\u00e1ch t\u00ecm g\u1ed3m c\u00e1c b\u01b0\u1edbc:<\/p>\n<ul>\n<li>T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh, x\u00e1c \u0111\u1ecbnh c\u00e1c \u0111i\u1ec3m l\u00e0m m\u1eabu s\u1ed1 b\u1eb1ng 0.<\/li>\n<li>Ki\u1ec3m tra t\u1eed s\u1ed1 t\u1ea1i \u0111i\u1ec3m \u0111\u00f3 kh\u00e1c 0.<\/li>\n<li>T\u00ednh gi\u1edbi h\u1ea1n m\u1ed9t b\u00ean \u0111\u1ec3 kh\u1eb3ng \u0111\u1ecbnh gi\u00e1 tr\u1ecb ti\u1ebfn ra v\u00f4 c\u1ef1c.<\/li>\n<\/ul>\n<p>V\u00ed d\u1ee5, h\u00e0m y = 1\/(x \u2212 2) c\u00f3 m\u1eabu b\u1eb1ng 0 t\u1ea1i x = 2, t\u1eed s\u1ed1 b\u1eb1ng 1 kh\u00e1c 0, n\u00ean \u0111\u1ed3 th\u1ecb c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = 2.<\/p>\n<h2>Ti\u1ec7m c\u1eadn ngang l\u00e0 g\u00ec v\u00e0 c\u00e1ch t\u00ecm<\/h2>\n<p>\u0110\u01b0\u1eddng th\u1eb3ng y = b \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 <strong>ti\u1ec7m c\u1eadn ngang<\/strong> c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f(x) n\u1ebfu:<\/p>\n<p><strong>lim f(x) = b khi x \u2192 +\u221e ho\u1eb7c x \u2192 \u2212\u221e<\/strong><\/p>\n<p>Ngh\u0129a l\u00e0 khi x ti\u1ebfn ra v\u00f4 c\u1ef1c, gi\u00e1 tr\u1ecb h\u00e0m s\u1ed1 ti\u1ebfn d\u1ea7n \u0111\u1ebfn h\u1eb1ng s\u1ed1 b. \u0110\u1ec3 t\u00ecm ti\u1ec7m c\u1eadn ngang, b\u1ea1n t\u00ednh gi\u1edbi h\u1ea1n c\u1ee7a h\u00e0m s\u1ed1 khi x \u2192 \u00b1\u221e; n\u1ebfu gi\u1edbi h\u1ea1n ra m\u1ed9t s\u1ed1 h\u1eefu h\u1ea1n b th\u00ec y = b l\u00e0 ti\u1ec7m c\u1eadn ngang.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-570827\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-2.jpg\" alt=\"duong-tiem-can-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>V\u00ed d\u1ee5, h\u00e0m y = 1\/x c\u00f3 ti\u1ec7m c\u1eadn ngang y = 0, v\u00ec khi x ti\u1ebfn ra v\u00f4 c\u1ef1c th\u00ec 1\/x ti\u1ebfn v\u1ec1 0. V\u1edbi h\u00e0m y = (2x + 1)\/(x + 3), khi x \u2192 \u00b1\u221e th\u00ec y ti\u1ebfn v\u1ec1 t\u1ec9 s\u1ed1 h\u1ec7 s\u1ed1 c\u1ee7a x, t\u1ee9c y = 2 l\u00e0 ti\u1ec7m c\u1eadn ngang.<\/p>\n<h2>Ti\u1ec7m c\u1eadn xi\u00ean l\u00e0 g\u00ec v\u00e0 c\u00e1ch t\u00ecm<\/h2>\n<p>\u0110\u01b0\u1eddng th\u1eb3ng y = ax + b (v\u1edbi a \u2260 0) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 <strong>ti\u1ec7m c\u1eadn xi\u00ean<\/strong> c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f(x) n\u1ebfu:<\/p>\n<p><strong>lim [f(x) \u2212 (ax + b)] = 0 khi x \u2192 +\u221e ho\u1eb7c x \u2192 \u2212\u221e<\/strong><\/p>\n<p>V\u1edbi h\u00e0m ph\u00e2n th\u1ee9c h\u1eefu t\u1ec9, ti\u1ec7m c\u1eadn xi\u00ean xu\u1ea5t hi\u1ec7n khi b\u1eadc c\u1ee7a t\u1eed s\u1ed1 l\u1edbn h\u01a1n b\u1eadc c\u1ee7a m\u1eabu s\u1ed1 \u0111\u00fang 1 \u0111\u01a1n v\u1ecb. Khi \u0111\u00f3 ta th\u1ef1c hi\u1ec7n ph\u00e9p chia \u0111a th\u1ee9c \u0111\u1ec3 \u0111\u01b0a h\u00e0m v\u1ec1 d\u1ea1ng y = ax + b + ph\u1ea7n d\u01b0\/m\u1eabu; ph\u1ea7n th\u01b0\u01a1ng ax + b ch\u00ednh l\u00e0 ti\u1ec7m c\u1eadn xi\u00ean. L\u01b0u \u00fd m\u1ed9t \u0111\u1ed3 th\u1ecb kh\u00f4ng th\u1ec3 v\u1eeba c\u00f3 ti\u1ec7m c\u1eadn ngang v\u1eeba c\u00f3 ti\u1ec7m c\u1eadn xi\u00ean \u1edf c\u00f9ng m\u1ed9t nh\u00e1nh.<\/p>\n<p>B\u1ea3ng d\u01b0\u1edbi \u0111\u00e2y t\u1ed5ng h\u1ee3p c\u00e1ch nh\u1eadn bi\u1ebft ba lo\u1ea1i ti\u1ec7m c\u1eadn cho h\u00e0m ph\u00e2n th\u1ee9c:<\/p>\n<table>\n<thead>\n<tr>\n<th>Lo\u1ea1i ti\u1ec7m c\u1eadn<\/th>\n<th>\u0110i\u1ec1u ki\u1ec7n nh\u1eadn bi\u1ebft<\/th>\n<th>C\u00e1ch x\u00e1c \u0111\u1ecbnh<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Ti\u1ec7m c\u1eadn \u0111\u1ee9ng<\/td>\n<td>M\u1eabu s\u1ed1 b\u1eb1ng 0, t\u1eed s\u1ed1 kh\u00e1c 0<\/td>\n<td>x = nghi\u1ec7m c\u1ee7a m\u1eabu s\u1ed1<\/td>\n<\/tr>\n<tr>\n<td>Ti\u1ec7m c\u1eadn ngang<\/td>\n<td>B\u1eadc t\u1eed \u2264 b\u1eadc m\u1eabu<\/td>\n<td>T\u00ednh lim f(x) khi x \u2192 \u00b1\u221e<\/td>\n<\/tr>\n<tr>\n<td>Ti\u1ec7m c\u1eadn xi\u00ean<\/td>\n<td>B\u1eadc t\u1eed l\u1edbn h\u01a1n b\u1eadc m\u1eabu 1 \u0111\u01a1n v\u1ecb<\/td>\n<td>Chia \u0111a th\u1ee9c l\u1ea5y ph\u1ea7n th\u01b0\u01a1ng ax + b<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>V\u1edbi h\u00e0m ph\u00e2n th\u1ee9c b\u1eadc nh\u1ea5t y = (ax + b)\/(cx + d), trong \u0111\u00f3 c \u2260 0 v\u00e0 ad \u2212 bc \u2260 0, ta c\u00f3 c\u00f4ng th\u1ee9c nhanh: ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = \u2212d\/c v\u00e0 ti\u1ec7m c\u1eadn ngang y = a\/c.<\/p>\n<h2>C\u00e1c b\u01b0\u1edbc t\u00ecm ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1<\/h2>\n<p>Quy tr\u00ecnh chung \u0111\u1ec3 t\u00ecm m\u1ecdi \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1 g\u1ed3m b\u1ed1n b\u01b0\u1edbc:<\/p>\n<ul>\n<li>B\u01b0\u1edbc 1: T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1.<\/li>\n<li>B\u01b0\u1edbc 2: T\u00ednh gi\u1edbi h\u1ea1n khi x \u2192 \u00b1\u221e \u0111\u1ec3 t\u00ecm ti\u1ec7m c\u1eadn ngang (n\u1ebfu c\u00f3).<\/li>\n<li>B\u01b0\u1edbc 3: X\u00e9t c\u00e1c \u0111i\u1ec3m kh\u00f4ng thu\u1ed9c t\u1eadp x\u00e1c \u0111\u1ecbnh (nghi\u1ec7m c\u1ee7a m\u1eabu s\u1ed1), t\u00ednh gi\u1edbi h\u1ea1n m\u1ed9t b\u00ean \u0111\u1ec3 t\u00ecm ti\u1ec7m c\u1eadn \u0111\u1ee9ng.<\/li>\n<li>B\u01b0\u1edbc 4: N\u1ebfu b\u1eadc t\u1eed l\u1edbn h\u01a1n b\u1eadc m\u1eabu 1 \u0111\u01a1n v\u1ecb, chia \u0111a th\u1ee9c \u0111\u1ec3 t\u00ecm ti\u1ec7m c\u1eadn xi\u00ean, r\u1ed3i k\u1ebft lu\u1eadn.<\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-570829\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-4.jpg\" alt=\"duong-tiem-can-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>Vi\u1ec7c t\u00ecm ti\u1ec7m c\u1eadn th\u01b0\u1eddng \u0111i k\u00e8m v\u1edbi x\u00e9t <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tinh-don-dieu-cua-ham-so\/\">t\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1<\/a> \u0111\u1ec3 ho\u00e0n thi\u1ec7n b\u1ea3ng bi\u1ebfn thi\u00ean khi kh\u1ea3o s\u00e1t \u0111\u1ed3 th\u1ecb.<\/p>\n<h2>V\u00ed d\u1ee5 t\u1ed5ng h\u1ee3p c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<p>X\u00e9t k\u1ef9 m\u1ed9t v\u00ed d\u1ee5 \u0111\u1ea7y \u0111\u1ee7 gi\u00fap b\u1ea1n gh\u00e9p n\u1ed1i c\u00e1c b\u01b0\u1edbc tr\u00ean. T\u00ecm c\u00e1c \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn c\u1ee7a h\u00e0m s\u1ed1 y = (2x + 1)\/(x \u2212 1).<\/p>\n<ul>\n<li><strong>B\u01b0\u1edbc 1 \u2013 T\u1eadp x\u00e1c \u0111\u1ecbnh:<\/strong> m\u1eabu x \u2212 1 = 0 khi x = 1, n\u00ean t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 R \\ {1}.<\/li>\n<li><strong>B\u01b0\u1edbc 2 \u2013 Ti\u1ec7m c\u1eadn ngang:<\/strong> lim y khi x \u2192 \u00b1\u221e b\u1eb1ng t\u1ec9 s\u1ed1 h\u1ec7 s\u1ed1 c\u1ee7a x, t\u1ee9c 2\/1 = 2. V\u1eady y = 2 l\u00e0 ti\u1ec7m c\u1eadn ngang.<\/li>\n<li><strong>B\u01b0\u1edbc 3 \u2013 Ti\u1ec7m c\u1eadn \u0111\u1ee9ng:<\/strong> t\u1ea1i x = 1, t\u1eed s\u1ed1 b\u1eb1ng 2(1) + 1 = 3 \u2260 0; gi\u1edbi h\u1ea1n m\u1ed9t b\u00ean c\u1ee7a y khi x \u2192 1 l\u00e0 v\u00f4 c\u1ef1c. V\u1eady x = 1 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng.<\/li>\n<li><strong>B\u01b0\u1edbc 4 \u2013 K\u1ebft lu\u1eadn:<\/strong> \u0111\u1ed3 th\u1ecb c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = 1 v\u00e0 ti\u1ec7m c\u1eadn ngang y = 2; kh\u00f4ng c\u00f3 ti\u1ec7m c\u1eadn xi\u00ean v\u00ec b\u1eadc t\u1eed b\u1eb1ng b\u1eadc m\u1eabu.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-570828\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-3.jpg\" alt=\"duong-tiem-can-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tiem-can-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>B\u1ea1n c\u00f3 th\u1ec3 luy\u1ec7n th\u00eam v\u1edbi h\u00e0m y = (3x \u2212 1)\/(x + 2): ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = \u22122, ti\u1ec7m c\u1eadn ngang y = 3. Ho\u1eb7c h\u00e0m y = (x\u00b2 + 1)\/(x \u2212 1) c\u00f3 b\u1eadc t\u1eed l\u1edbn h\u01a1n m\u1eabu 1 \u0111\u01a1n v\u1ecb n\u00ean s\u1ebd xu\u1ea5t hi\u1ec7n ti\u1ec7m c\u1eadn xi\u00ean. C\u00e1ch x\u1eed l\u00fd t\u01b0\u01a1ng t\u1ef1 khi kh\u1ea3o s\u00e1t <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/ham-so-bac-2-la-gi\/\">h\u00e0m s\u1ed1 b\u1eadc 2<\/a> v\u00e0 c\u00e1c d\u1ea1ng \u0111\u1ed3 th\u1ecb kh\u00e1c.<\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn<\/h2>\n<h3>\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn l\u00e0 g\u00ec?<\/h3>\n<p>\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng m\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ti\u1ebfn s\u00e1t khi bi\u1ebfn s\u1ed1 ho\u1eb7c gi\u00e1 tr\u1ecb h\u00e0m s\u1ed1 ti\u1ebfn ra v\u00f4 c\u1ef1c, th\u01b0\u1eddng kh\u00f4ng c\u1eaft ho\u1eb7c ch\u1ec9 c\u1eaft t\u1ea1i h\u1eefu h\u1ea1n \u0111i\u1ec3m.<\/p>\n<h3>C\u00f3 m\u1ea5y lo\u1ea1i \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn?<\/h3>\n<p>C\u00f3 ba lo\u1ea1i: ti\u1ec7m c\u1eadn \u0111\u1ee9ng (x = a), ti\u1ec7m c\u1eadn ngang (y = b) v\u00e0 ti\u1ec7m c\u1eadn xi\u00ean (y = ax + b v\u1edbi a \u2260 0).<\/p>\n<h3>C\u00e1ch t\u00ecm ti\u1ec7m c\u1eadn \u0111\u1ee9ng th\u1ebf n\u00e0o?<\/h3>\n<p>T\u00ecm c\u00e1c \u0111i\u1ec3m l\u00e0m m\u1eabu s\u1ed1 b\u1eb1ng 0 m\u00e0 t\u1eed s\u1ed1 kh\u00e1c 0, sau \u0111\u00f3 ki\u1ec3m tra gi\u1edbi h\u1ea1n m\u1ed9t b\u00ean c\u1ee7a h\u00e0m s\u1ed1 t\u1ea1i \u0111i\u1ec3m \u0111\u00f3 ra v\u00f4 c\u1ef1c th\u00ec \u0111\u00f3 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng.<\/p>\n<h3>C\u00e1ch t\u00ecm ti\u1ec7m c\u1eadn ngang th\u1ebf n\u00e0o?<\/h3>\n<p>T\u00ednh gi\u1edbi h\u1ea1n c\u1ee7a h\u00e0m s\u1ed1 khi x ti\u1ebfn ra \u00b1\u221e; n\u1ebfu gi\u1edbi h\u1ea1n ra m\u1ed9t s\u1ed1 h\u1eefu h\u1ea1n b th\u00ec y = b l\u00e0 ti\u1ec7m c\u1eadn ngang.<\/p>\n<h3>Khi n\u00e0o \u0111\u1ed3 th\u1ecb c\u00f3 ti\u1ec7m c\u1eadn xi\u00ean?<\/h3>\n<p>V\u1edbi h\u00e0m ph\u00e2n th\u1ee9c, \u0111\u1ed3 th\u1ecb c\u00f3 ti\u1ec7m c\u1eadn xi\u00ean khi b\u1eadc c\u1ee7a t\u1eed s\u1ed1 l\u1edbn h\u01a1n b\u1eadc c\u1ee7a m\u1eabu s\u1ed1 \u0111\u00fang 1 \u0111\u01a1n v\u1ecb.<\/p>\n<h3>H\u00e0m y = (ax + b)\/(cx + d) c\u00f3 ti\u1ec7m c\u1eadn n\u00e0o?<\/h3>\n<p>H\u00e0m n\u00e0y c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = \u2212d\/c v\u00e0 ti\u1ec7m c\u1eadn ngang y = a\/c, v\u1edbi \u0111i\u1ec1u ki\u1ec7n c \u2260 0 v\u00e0 ad \u2212 bc \u2260 0.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>T\u00f3m l\u1ea1i, <strong>\u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn g\u1ed3m ti\u1ec7m c\u1eadn \u0111\u1ee9ng (x = a), ti\u1ec7m c\u1eadn ngang (y = b) v\u00e0 ti\u1ec7m c\u1eadn xi\u00ean (y = ax + b); ri\u00eang h\u00e0m (ax+b)\/(cx+d) c\u00f3 x = \u2212d\/c v\u00e0 y = a\/c<\/strong>. N\u1eafm v\u1eefng quy tr\u00ecnh b\u1ed1n b\u01b0\u1edbc v\u00e0 luy\u1ec7n t\u1eadp qua v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i s\u1ebd gi\u00fap b\u1ea1n t\u00ecm ti\u1ec7m c\u1eadn nhanh, ch\u00ednh x\u00e1c v\u00e0 t\u1ef1 tin h\u01a1n khi kh\u1ea3o s\u00e1t, v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 trong c\u00e1c b\u00e0i ki\u1ec3m tra v\u00e0 k\u1ef3 thi.<br \/>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [\n    {\n      \"@type\": \"Question\",\n      \"name\": \"\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng m\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ti\u1ebfn s\u00e1t khi bi\u1ebfn s\u1ed1 ho\u1eb7c gi\u00e1 tr\u1ecb h\u00e0m s\u1ed1 ti\u1ebfn ra v\u00f4 c\u1ef1c, th\u01b0\u1eddng kh\u00f4ng c\u1eaft ho\u1eb7c ch\u1ec9 c\u1eaft t\u1ea1i h\u1eefu h\u1ea1n \u0111i\u1ec3m.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00f3 m\u1ea5y lo\u1ea1i \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"C\u00f3 ba lo\u1ea1i: ti\u1ec7m c\u1eadn \u0111\u1ee9ng (x = a), ti\u1ec7m c\u1eadn ngang (y = b) v\u00e0 ti\u1ec7m c\u1eadn xi\u00ean (y = ax + b v\u1edbi a kh\u00e1c 0).\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00e1ch t\u00ecm ti\u1ec7m c\u1eadn \u0111\u1ee9ng th\u1ebf n\u00e0o?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"T\u00ecm c\u00e1c \u0111i\u1ec3m l\u00e0m m\u1eabu s\u1ed1 b\u1eb1ng 0 m\u00e0 t\u1eed s\u1ed1 kh\u00e1c 0, sau \u0111\u00f3 ki\u1ec3m tra gi\u1edbi h\u1ea1n m\u1ed9t b\u00ean c\u1ee7a h\u00e0m s\u1ed1 t\u1ea1i \u0111i\u1ec3m \u0111\u00f3 ra v\u00f4 c\u1ef1c th\u00ec \u0111\u00f3 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00e1ch t\u00ecm ti\u1ec7m c\u1eadn ngang th\u1ebf n\u00e0o?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"T\u00ednh gi\u1edbi h\u1ea1n c\u1ee7a h\u00e0m s\u1ed1 khi x ti\u1ebfn ra v\u00f4 c\u1ef1c; n\u1ebfu gi\u1edbi h\u1ea1n ra m\u1ed9t s\u1ed1 h\u1eefu h\u1ea1n b th\u00ec y = b l\u00e0 ti\u1ec7m c\u1eadn ngang.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Khi n\u00e0o \u0111\u1ed3 th\u1ecb c\u00f3 ti\u1ec7m c\u1eadn xi\u00ean?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"V\u1edbi h\u00e0m ph\u00e2n th\u1ee9c, \u0111\u1ed3 th\u1ecb c\u00f3 ti\u1ec7m c\u1eadn xi\u00ean khi b\u1eadc c\u1ee7a t\u1eed s\u1ed1 l\u1edbn h\u01a1n b\u1eadc c\u1ee7a m\u1eabu s\u1ed1 \u0111\u00fang 1 \u0111\u01a1n v\u1ecb.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"H\u00e0m y = (ax + b)\/(cx + d) c\u00f3 ti\u1ec7m c\u1eadn n\u00e0o?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"H\u00e0m n\u00e0y c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = -d\/c v\u00e0 ti\u1ec7m c\u1eadn ngang y = a\/c, v\u1edbi \u0111i\u1ec1u ki\u1ec7n c kh\u00e1c 0 v\u00e0 ad - bc kh\u00e1c 0.\"\n      }\n    }\n  ]\n}\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng m\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m tr\u00ean \u0111\u1ed3 th\u1ecb \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3 d\u1ea7n ti\u1ebfn v\u1ec1 0 khi \u0111i\u1ec3m ch\u1ea1y ra xa v\u00f4 t\u1eadn. Ba lo\u1ea1i th\u01b0\u1eddng g\u1eb7p l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng, ti\u1ec7m c\u1eadn ngang v\u00e0 ti\u1ec7m c\u1eadn xi\u00ean. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c n\u1ec1n c\u1ee7a [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":570830,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"\u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn l\u00e0 g\u00ec","_yoast_wpseo_title":"\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn l\u00e0 g\u00ec? C\u00e1ch t\u00ecm ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0 ti\u1ec7m c\u1eadn ngang","_yoast_wpseo_metadesc":"\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn l\u00e0 g\u00ec? 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