{"id":620585,"date":"2026-11-09T09:12:51","date_gmt":"2026-11-09T02:12:51","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=620585"},"modified":"2026-11-09T09:12:51","modified_gmt":"2026-11-09T02:12:51","slug":"lap-bang-bien-thien","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/lap-bang-bien-thien\/","title":{"rendered":"L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean: c\u00e1c b\u01b0\u1edbc v\u00e0 v\u00ed d\u1ee5 cho t\u1eebng d\u1ea1ng h\u00e0m s\u1ed1"},"content":{"rendered":"<p>L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean l\u00e0 tr\u00ecnh b\u00e0y g\u1ecdn trong m\u1ed9t b\u1ea3ng kho\u1ea3ng \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn, c\u1ef1c tr\u1ecb v\u00e0 gi\u1edbi h\u1ea1n c\u1ee7a h\u00e0m s\u1ed1, g\u1ed3m 4 b\u01b0\u1edbc: t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh, t\u00ednh \u0111\u1ea1o h\u00e0m y&#8217;, t\u00ecm c\u00e1c \u0111i\u1ec3m y&#8217; = 0 ho\u1eb7c kh\u00f4ng x\u00e1c \u0111\u1ecbnh, r\u1ed3i x\u00e9t d\u1ea5u y&#8217; v\u00e0 \u0111i\u1ec1n m\u0169i t\u00ean l\u00ean xu\u1ed1ng cho y. V\u1edbi h\u00e0m b\u1eadc hai (l\u1edbp 10) c\u00f3 th\u1ec3 l\u1eadp b\u1ea3ng ngay t\u1eeb t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh m\u00e0 kh\u00f4ng c\u1ea7n \u0111\u1ea1o h\u00e0m. B\u00e0i vi\u1ebft c\u00f3 4 v\u00ed d\u1ee5 l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean chi ti\u1ebft cho c\u00e1c d\u1ea1ng h\u00e0m hay g\u1eb7p.<\/p>\n<h2>B\u1ea3ng bi\u1ebfn thi\u00ean l\u00e0 g\u00ec?<\/h2>\n<p>B\u1ea3ng bi\u1ebfn thi\u00ean l\u00e0 b\u1ea3ng t\u00f3m t\u1eaft s\u1ef1 t\u0103ng, gi\u1ea3m c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean t\u1eebng kho\u1ea3ng c\u1ee7a t\u1eadp x\u00e1c \u0111\u1ecbnh, k\u00e8m c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1eb7c bi\u1ec7t nh\u01b0 c\u1ef1c \u0111\u1ea1i, c\u1ef1c ti\u1ec3u v\u00e0 gi\u1edbi h\u1ea1n. Nh\u00ecn b\u1ea3ng bi\u1ebfn thi\u00ean, b\u1ea1n bi\u1ebft ngay h\u00e0m \u0111\u1ed3ng bi\u1ebfn hay ngh\u1ecbch bi\u1ebfn \u1edf \u0111\u00e2u, \u0111\u1ea1t c\u1ef1c tr\u1ecb t\u1ea1i \u0111i\u1ec3m n\u00e0o m\u00e0 kh\u00f4ng c\u1ea7n v\u1ebd \u0111\u1ed3 th\u1ecb.<\/p>\n<p>M\u1ed9t b\u1ea3ng bi\u1ebfn thi\u00ean th\u01b0\u1eddng c\u00f3 ba d\u00f2ng:<\/p>\n<ul>\n<li>D\u00f2ng x: c\u00e1c m\u1ed1c quan tr\u1ecdng theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n: \u2212\u221e, \u0111i\u1ec3m t\u1edbi h\u1ea1n, \u0111i\u1ec3m kh\u00f4ng x\u00e1c \u0111\u1ecbnh, +\u221e.<\/li>\n<li>D\u00f2ng y&#8217;: d\u1ea5u c\u1ee7a \u0111\u1ea1o h\u00e0m tr\u00ean t\u1eebng kho\u1ea3ng (+ ho\u1eb7c \u2212), ghi 0 t\u1ea1i \u0111i\u1ec3m y&#8217; = 0, ghi d\u1ea5u || t\u1ea1i \u0111i\u1ec3m kh\u00f4ng x\u00e1c \u0111\u1ecbnh.<\/li>\n<li>D\u00f2ng y: m\u0169i t\u00ean \u0111i l\u00ean (\u2197) n\u1ebfu y&#8217; &gt; 0, \u0111i xu\u1ed1ng (\u2198) n\u1ebfu y&#8217; &lt; 0, k\u00e8m gi\u00e1 tr\u1ecb c\u1ee7a h\u00e0m t\u1ea1i c\u00e1c m\u1ed1c v\u00e0 gi\u1edbi h\u1ea1n.<\/li>\n<\/ul>\n<p>Trong ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi, b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m b\u1eadc hai \u0111\u01b0\u1ee3c h\u1ecdc \u1edf l\u1edbp 10; c\u00e1ch d\u00f9ng \u0111\u1ea1o h\u00e0m \u0111\u1ec3 x\u00e9t t\u00ednh \u0111\u01a1n \u0111i\u1ec7u h\u1ecdc \u1edf l\u1edbp 12. N\u1ebfu ch\u01b0a v\u1eefng ph\u1ea7n \u0111\u1ea1o h\u00e0m, xem l\u1ea1i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dao-ham-lop-11\/\">b\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m<\/a>.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-622474 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-1.jpg\" alt=\"lap-bang-bien-thien-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1c b\u01b0\u1edbc l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1<\/h2>\n<p>C\u00e1ch l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 g\u1ed3m 4 b\u01b0\u1edbc theo th\u1ee9 t\u1ef1: t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh, t\u00ednh \u0111\u1ea1o h\u00e0m v\u00e0 nghi\u1ec7m c\u1ee7a y&#8217;, t\u00ednh gi\u1edbi h\u1ea1n, r\u1ed3i \u0111i\u1ec1n b\u1ea3ng v\u00e0 k\u1ebft lu\u1eadn. L\u00e0m \u0111\u1ee7 4 b\u01b0\u1edbc gi\u00fap tr\u00e1nh s\u00f3t kho\u1ea3ng ho\u1eb7c sai chi\u1ec1u m\u0169i t\u00ean.<\/p>\n<ol>\n<li>T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh D. V\u1edbi ph\u00e2n th\u1ee9c, lo\u1ea1i c\u00e1c gi\u00e1 tr\u1ecb l\u00e0m m\u1eabu b\u1eb1ng 0; v\u1edbi c\u0103n b\u1eadc ch\u1eb5n, bi\u1ec3u th\u1ee9c trong c\u0103n ph\u1ea3i kh\u00f4ng \u00e2m.<\/li>\n<li>T\u00ednh y&#8217; v\u00e0 gi\u1ea3i y&#8217; = 0. Ghi th\u00eam c\u00e1c \u0111i\u1ec3m thu\u1ed9c D m\u00e0 y&#8217; kh\u00f4ng x\u00e1c \u0111\u1ecbnh.<\/li>\n<li>T\u00ednh gi\u1edbi h\u1ea1n c\u1ee7a y khi x \u2192 \u2212\u221e, x \u2192 +\u221e v\u00e0 khi x ti\u1ebfn v\u1ec1 c\u00e1c \u0111i\u1ec3m kh\u00f4ng thu\u1ed9c D.<\/li>\n<li>X\u00e9t d\u1ea5u y&#8217; tr\u00ean t\u1eebng kho\u1ea3ng b\u1eb1ng c\u00e1ch th\u1eed m\u1ed9t gi\u00e1 tr\u1ecb b\u1ea5t k\u1ef3 trong kho\u1ea3ng, ho\u1eb7c d\u00f9ng quy t\u1eafc d\u1ea5u c\u1ee7a tam th\u1ee9c b\u1eadc hai.<\/li>\n<li>\u0110i\u1ec1n b\u1ea3ng v\u00e0 k\u1ebft lu\u1eadn kho\u1ea3ng \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn, c\u1ef1c \u0111\u1ea1i, c\u1ef1c ti\u1ec3u.<\/li>\n<\/ol>\n<p><img decoding=\"async\" class=\"size-full wp-image-622475 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-2.jpg\" alt=\"lap-bang-bien-thien-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean h\u00e0m s\u1ed1 b\u1eadc hai<\/h2>\n<p>V\u1edbi h\u00e0m s\u1ed1 b\u1eadc hai y = ax\u00b2 + bx + c, b\u1ea3ng bi\u1ebfn thi\u00ean \u0111\u01b0\u1ee3c l\u1eadp t\u1eeb t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh I(\u2212b\/2a; \u2212\u0394\/4a): n\u1ebfu a &gt; 0, h\u00e0m ngh\u1ecbch bi\u1ebfn tr\u01b0\u1edbc \u0111\u1ec9nh v\u00e0 \u0111\u1ed3ng bi\u1ebfn sau \u0111\u1ec9nh; n\u1ebfu a &lt; 0 th\u00ec ng\u01b0\u1ee3c l\u1ea1i.<\/p>\n<p>V\u00ed d\u1ee5 1: L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 y = x\u00b2 \u2212 4x + 3.<\/p>\n<ul>\n<li>a = 1 &gt; 0, ho\u00e0nh \u0111\u1ed9 \u0111\u1ec9nh x = \u2212b\/(2a) = 4\/2 = 2.<\/li>\n<li>Tung \u0111\u1ed9 \u0111\u1ec9nh y(2) = 4 \u2212 8 + 3 = \u22121.<\/li>\n<\/ul>\n<table>\n<thead>\n<tr>\n<th>x<\/th>\n<th>\u2212\u221e<\/th>\n<th><\/th>\n<th>2<\/th>\n<th><\/th>\n<th>+\u221e<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>y<\/td>\n<td>+\u221e<\/td>\n<td>\u2198<\/td>\n<td>\u22121<\/td>\n<td>\u2197<\/td>\n<td>+\u221e<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>K\u1ebft lu\u1eadn: h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean (\u2212\u221e; 2), \u0111\u1ed3ng bi\u1ebfn tr\u00ean (2; +\u221e), \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t b\u1eb1ng \u22121 t\u1ea1i x = 2. Xem th\u00eam v\u1ec1 \u0111\u1ec9nh v\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng trong b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/ham-so-bac-2-la-gi\/\">h\u00e0m s\u1ed1 b\u1eadc 2<\/a>.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-622476 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-3.jpg\" alt=\"lap-bang-bien-thien-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean h\u00e0m s\u1ed1 b\u1eadc ba<\/h2>\n<p>V\u1edbi h\u00e0m b\u1eadc ba, t\u00ednh y&#8217; (l\u00e0 tam th\u1ee9c b\u1eadc hai), t\u00ecm nghi\u1ec7m c\u1ee7a y&#8217; = 0, x\u00e9t d\u1ea5u y&#8217; r\u1ed3i \u0111i\u1ec1n b\u1ea3ng; n\u1ebfu y&#8217; c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t, h\u00e0m c\u00f3 m\u1ed9t c\u1ef1c \u0111\u1ea1i v\u00e0 m\u1ed9t c\u1ef1c ti\u1ec3u.<\/p>\n<p>V\u00ed d\u1ee5 2: L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 y = x\u00b3 \u2212 3x\u00b2 + 2.<\/p>\n<ul>\n<li>T\u1eadp x\u00e1c \u0111\u1ecbnh D = \u211d.<\/li>\n<li>y&#8217; = 3x\u00b2 \u2212 6x = 3x(x \u2212 2); y&#8217; = 0 \u21d4 x = 0 ho\u1eb7c x = 2.<\/li>\n<li>y(0) = 2; y(2) = 8 \u2212 12 + 2 = \u22122.<\/li>\n<li>Gi\u1edbi h\u1ea1n: x \u2192 \u2212\u221e th\u00ec y \u2192 \u2212\u221e; x \u2192 +\u221e th\u00ec y \u2192 +\u221e.<\/li>\n<li>D\u1ea5u y&#8217;: d\u01b0\u01a1ng tr\u00ean (\u2212\u221e; 0), \u00e2m tr\u00ean (0; 2), d\u01b0\u01a1ng tr\u00ean (2; +\u221e).<\/li>\n<\/ul>\n<table>\n<thead>\n<tr>\n<th>x<\/th>\n<th>\u2212\u221e<\/th>\n<th><\/th>\n<th>0<\/th>\n<th><\/th>\n<th>2<\/th>\n<th><\/th>\n<th>+\u221e<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>y&#8217;<\/td>\n<td><\/td>\n<td>+<\/td>\n<td>0<\/td>\n<td>\u2212<\/td>\n<td>0<\/td>\n<td>+<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>y<\/td>\n<td>\u2212\u221e<\/td>\n<td>\u2197<\/td>\n<td>2<\/td>\n<td>\u2198<\/td>\n<td>\u22122<\/td>\n<td>\u2197<\/td>\n<td>+\u221e<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>K\u1ebft lu\u1eadn: h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean (\u2212\u221e; 0) v\u00e0 (2; +\u221e), ngh\u1ecbch bi\u1ebfn tr\u00ean (0; 2); \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i y = 2 t\u1ea1i x = 0 v\u00e0 c\u1ef1c ti\u1ec3u y = \u22122 t\u1ea1i x = 2.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-622477 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-4.jpg\" alt=\"lap-bang-bien-thien-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean h\u00e0m tr\u00f9ng ph\u01b0\u01a1ng (b\u1eadc b\u1ed1n)<\/h2>\n<p>H\u00e0m tr\u00f9ng ph\u01b0\u01a1ng y = ax\u2074 + bx\u00b2 + c c\u00f3 y&#8217; = 4ax\u00b3 + 2bx = 2x(2ax\u00b2 + b); n\u1ebfu a v\u00e0 b tr\u00e1i d\u1ea5u, y&#8217; c\u00f3 ba nghi\u1ec7m v\u00e0 b\u1ea3ng bi\u1ebfn thi\u00ean c\u00f3 ba c\u1ef1c tr\u1ecb v\u1edbi d\u1ea1ng ch\u1eef W (a &gt; 0) ho\u1eb7c ch\u1eef M (a &lt; 0).<\/p>\n<p>V\u00ed d\u1ee5 3: L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 y = x\u2074 \u2212 2x\u00b2 + 1.<\/p>\n<ul>\n<li>y&#8217; = 4x\u00b3 \u2212 4x = 4x(x\u00b2 \u2212 1); y&#8217; = 0 \u21d4 x = \u22121, x = 0, x = 1.<\/li>\n<li>y(\u22121) = 0; y(0) = 1; y(1) = 0. Khi x \u2192 \u00b1\u221e th\u00ec y \u2192 +\u221e.<\/li>\n<li>D\u1ea5u y&#8217;: \u00e2m tr\u00ean (\u2212\u221e; \u22121), d\u01b0\u01a1ng tr\u00ean (\u22121; 0), \u00e2m tr\u00ean (0; 1), d\u01b0\u01a1ng tr\u00ean (1; +\u221e).<\/li>\n<\/ul>\n<table>\n<thead>\n<tr>\n<th>x<\/th>\n<th>\u2212\u221e<\/th>\n<th><\/th>\n<th>\u22121<\/th>\n<th><\/th>\n<th>0<\/th>\n<th><\/th>\n<th>1<\/th>\n<th><\/th>\n<th>+\u221e<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>y&#8217;<\/td>\n<td><\/td>\n<td>\u2212<\/td>\n<td>0<\/td>\n<td>+<\/td>\n<td>0<\/td>\n<td>\u2212<\/td>\n<td>0<\/td>\n<td>+<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>y<\/td>\n<td>+\u221e<\/td>\n<td>\u2198<\/td>\n<td>0<\/td>\n<td>\u2197<\/td>\n<td>1<\/td>\n<td>\u2198<\/td>\n<td>0<\/td>\n<td>\u2197<\/td>\n<td>+\u221e<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>K\u1ebft lu\u1eadn: h\u00e0m \u0111\u1ea1t c\u1ef1c ti\u1ec3u y = 0 t\u1ea1i x = \u00b11 v\u00e0 c\u1ef1c \u0111\u1ea1i y = 1 t\u1ea1i x = 0.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-622478 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-5.jpg\" alt=\"lap-bang-bien-thien-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean h\u00e0m ph\u00e2n th\u1ee9c b\u1eadc nh\u1ea5t tr\u00ean b\u1eadc nh\u1ea5t<\/h2>\n<p>V\u1edbi h\u00e0m y = (ax + b)\/(cx + d), \u0111\u1ea1o h\u00e0m y&#8217; = (ad \u2212 bc)\/(cx + d)\u00b2 kh\u00f4ng \u0111\u1ed5i d\u1ea5u, n\u00ean h\u00e0m lu\u00f4n \u0111\u1ed3ng bi\u1ebfn ho\u1eb7c lu\u00f4n ngh\u1ecbch bi\u1ebfn tr\u00ean t\u1eebng kho\u1ea3ng x\u00e1c \u0111\u1ecbnh; b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ea7n ghi th\u00eam ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0 ti\u1ec7m c\u1eadn ngang.<\/p>\n<p>V\u00ed d\u1ee5 4: L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 y = (2x + 1)\/(x \u2212 1).<\/p>\n<ul>\n<li>T\u1eadp x\u00e1c \u0111\u1ecbnh D = \u211d \\ {1}.<\/li>\n<li>y&#8217; = (2\u00b7(\u22121) \u2212 1\u00b71)\/(x \u2212 1)\u00b2 = \u22123\/(x \u2212 1)\u00b2 &lt; 0 v\u1edbi m\u1ecdi x \u2260 1.<\/li>\n<li>Khi x \u2192 \u00b1\u221e, y \u2192 2 (ti\u1ec7m c\u1eadn ngang y = 2). Khi x \u2192 1\u207b, y \u2192 \u2212\u221e; khi x \u2192 1\u207a, y \u2192 +\u221e (ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = 1).<\/li>\n<\/ul>\n<table>\n<thead>\n<tr>\n<th>x<\/th>\n<th>\u2212\u221e<\/th>\n<th><\/th>\n<th>1<\/th>\n<th><\/th>\n<th>+\u221e<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>y&#8217;<\/td>\n<td><\/td>\n<td>\u2212<\/td>\n<td>||<\/td>\n<td>\u2212<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>y<\/td>\n<td>2<\/td>\n<td>\u2198 \u2212\u221e<\/td>\n<td>||<\/td>\n<td>+\u221e \u2198<\/td>\n<td>2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>K\u1ebft lu\u1eadn: h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean (\u2212\u221e; 1) v\u00e0 (1; +\u221e), kh\u00f4ng c\u00f3 c\u1ef1c tr\u1ecb. L\u01b0u \u00fd kh\u00f4ng vi\u1ebft &#8220;ngh\u1ecbch bi\u1ebfn tr\u00ean \u211d \\ {1}&#8221;, v\u00ec h\u00e0m ch\u1ec9 ngh\u1ecbch bi\u1ebfn tr\u00ean t\u1eebng kho\u1ea3ng ri\u00eang bi\u1ec7t.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-622479 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-6.jpg\" alt=\"lap-bang-bien-thien-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>\u0110\u1ecdc b\u1ea3ng bi\u1ebfn thi\u00ean \u0111\u1ec3 tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m<\/h2>\n<p>T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean, b\u1ea1n \u0111\u1ecdc \u0111\u01b0\u1ee3c 4 lo\u1ea1i th\u00f4ng tin hay g\u1eb7p trong \u0111\u1ec1 thi: kho\u1ea3ng \u0111\u01a1n \u0111i\u1ec7u, c\u1ef1c tr\u1ecb, gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t \u2013 nh\u1ecf nh\u1ea5t tr\u00ean m\u1ed9t \u0111o\u1ea1n v\u00e0 s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f(x) = m.<\/p>\n<table>\n<thead>\n<tr>\n<th>C\u00e2u h\u1ecfi<\/th>\n<th>C\u00e1ch \u0111\u1ecdc t\u1eeb b\u1ea3ng<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>H\u00e0m \u0111\u1ed3ng bi\u1ebfn tr\u00ean kho\u1ea3ng n\u00e0o?<\/td>\n<td>C\u00e1c kho\u1ea3ng c\u00f3 m\u0169i t\u00ean \u0111i l\u00ean (y&#8217; mang d\u1ea5u +)<\/td>\n<\/tr>\n<tr>\n<td>\u0110i\u1ec3m c\u1ef1c \u0111\u1ea1i, c\u1ef1c ti\u1ec3u?<\/td>\n<td>N\u01a1i m\u0169i t\u00ean \u0111\u1ed5i t\u1eeb l\u00ean sang xu\u1ed1ng (c\u1ef1c \u0111\u1ea1i) ho\u1eb7c xu\u1ed1ng sang l\u00ean (c\u1ef1c ti\u1ec3u)<\/td>\n<\/tr>\n<tr>\n<td>Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, nh\u1ecf nh\u1ea5t tr\u00ean \u0111o\u1ea1n [a; b]?<\/td>\n<td>So s\u00e1nh gi\u00e1 tr\u1ecb t\u1ea1i c\u1ef1c tr\u1ecb n\u1eb1m trong \u0111o\u1ea1n v\u00e0 t\u1ea1i hai \u0111\u1ea7u m\u00fat<\/td>\n<\/tr>\n<tr>\n<td>Ph\u01b0\u01a1ng tr\u00ecnh f(x) = m c\u00f3 m\u1ea5y nghi\u1ec7m?<\/td>\n<td>K\u1ebb \u0111\u01b0\u1eddng ngang y = m, \u0111\u1ebfm s\u1ed1 l\u1ea7n c\u1eaft c\u00e1c m\u0169i t\u00ean<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>V\u00ed d\u1ee5 v\u1edbi b\u1ea3ng \u1edf V\u00ed d\u1ee5 2, ph\u01b0\u01a1ng tr\u00ecnh x\u00b3 \u2212 3x\u00b2 + 2 = m c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t khi \u22122 &lt; m &lt; 2. Mu\u1ed1n \u00f4n k\u1ef9 h\u01a1n ph\u1ea7n \u0111\u1ed3ng bi\u1ebfn, ngh\u1ecbch bi\u1ebfn, xem b\u00e0i <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>.<\/p>\n<h2>L\u1ed7i th\u01b0\u1eddng g\u1eb7p khi l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean<\/h2>\n<p>C\u00e1c l\u1ed7i hay m\u1ea5t \u0111i\u1ec3m nh\u1ea5t l\u00e0 qu\u00ean t\u1eadp x\u00e1c \u0111\u1ecbnh, x\u00e9t d\u1ea5u y&#8217; sai \u1edf kho\u1ea3ng c\u00f3 nghi\u1ec7m k\u00e9p, d\u00f9ng d\u1ea5u h\u1ee3p &#8220;\u222a&#8221; khi k\u1ebft lu\u1eadn kho\u1ea3ng \u0111\u01a1n \u0111i\u1ec7u v\u00e0 qu\u00ean ghi gi\u1edbi h\u1ea1n t\u1ea1i ti\u1ec7m c\u1eadn \u0111\u1ee9ng.<\/p>\n<ul>\n<li>Nghi\u1ec7m k\u00e9p kh\u00f4ng \u0111\u1ed5i d\u1ea5u: v\u00ed d\u1ee5 y&#8217; = (x \u2212 1)\u00b2 th\u00ec y&#8217; kh\u00f4ng \u0111\u1ed5i d\u1ea5u khi qua x = 1, n\u00ean x = 1 kh\u00f4ng ph\u1ea3i c\u1ef1c tr\u1ecb.<\/li>\n<li>Vi\u1ebft kho\u1ea3ng b\u1eb1ng d\u1ea5u \u222a: k\u1ebft lu\u1eadn &#8220;\u0111\u1ed3ng bi\u1ebfn tr\u00ean (\u2212\u221e; 0) v\u00e0 (2; +\u221e)&#8221;, kh\u00f4ng vi\u1ebft &#8220;(\u2212\u221e; 0) \u222a (2; +\u221e)&#8221;.<\/li>\n<li>Sai th\u1ee9 t\u1ef1 m\u1ed1c: c\u00e1c gi\u00e1 tr\u1ecb tr\u00ean d\u00f2ng x ph\u1ea3i x\u1ebfp t\u0103ng d\u1ea7n.<\/li>\n<li>Thi\u1ebfu gi\u1edbi h\u1ea1n: b\u1ea3ng c\u1ee7a h\u00e0m ph\u00e2n th\u1ee9c ph\u1ea3i c\u00f3 gi\u1edbi h\u1ea1n \u1edf hai ph\u00eda c\u1ee7a ti\u1ec7m c\u1eadn \u0111\u1ee9ng.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-622480 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-7.jpg\" alt=\"lap-bang-bien-thien-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/lap-bang-bien-thien-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 c\u00e1ch l\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean<\/h2>\n<h3>L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean g\u1ed3m m\u1ea5y b\u01b0\u1edbc?<\/h3>\n<p>G\u1ed3m 4 b\u01b0\u1edbc: t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh, t\u00ednh \u0111\u1ea1o h\u00e0m v\u00e0 nghi\u1ec7m c\u1ee7a y&#8217;, t\u00ednh gi\u1edbi h\u1ea1n, r\u1ed3i x\u00e9t d\u1ea5u y&#8217; \u0111\u1ec3 \u0111i\u1ec1n b\u1ea3ng v\u00e0 k\u1ebft lu\u1eadn.<\/p>\n<h3>L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean l\u1edbp 10 c\u00f3 c\u1ea7n \u0111\u1ea1o h\u00e0m kh\u00f4ng?<\/h3>\n<p>Kh\u00f4ng. V\u1edbi h\u00e0m b\u1eadc hai \u1edf l\u1edbp 10, b\u1ea1n l\u1eadp b\u1ea3ng d\u1ef1a v\u00e0o h\u1ec7 s\u1ed1 a v\u00e0 t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh I(\u2212b\/2a; \u2212\u0394\/4a).<\/p>\n<h3>L\u00e0m sao bi\u1ebft m\u0169i t\u00ean \u0111i l\u00ean hay \u0111i xu\u1ed1ng?<\/h3>\n<p>Tr\u00ean kho\u1ea3ng y&#8217; mang d\u1ea5u +, m\u0169i t\u00ean \u0111i l\u00ean (h\u00e0m \u0111\u1ed3ng bi\u1ebfn); y&#8217; mang d\u1ea5u \u2212, m\u0169i t\u00ean \u0111i xu\u1ed1ng (h\u00e0m ngh\u1ecbch bi\u1ebfn).<\/p>\n<h3>Khi n\u00e0o m\u1ed9t \u0111i\u1ec3m l\u00e0 c\u1ef1c tr\u1ecb trong b\u1ea3ng bi\u1ebfn thi\u00ean?<\/h3>\n<p>Khi y&#8217; \u0111\u1ed5i d\u1ea5u qua \u0111i\u1ec3m \u0111\u00f3: t\u1eeb + sang \u2212 l\u00e0 c\u1ef1c \u0111\u1ea1i, t\u1eeb \u2212 sang + l\u00e0 c\u1ef1c ti\u1ec3u. N\u1ebfu y&#8217; b\u1eb1ng 0 nh\u01b0ng kh\u00f4ng \u0111\u1ed5i d\u1ea5u th\u00ec kh\u00f4ng ph\u1ea3i c\u1ef1c tr\u1ecb.<\/p>\n<h3>B\u1ea3ng bi\u1ebfn thi\u00ean h\u00e0m ph\u00e2n th\u1ee9c c\u00f3 g\u00ec kh\u00e1c?<\/h3>\n<p>C\u00f3 th\u00eam d\u1ea5u hai g\u1ea1ch t\u1ea1i \u0111i\u1ec3m h\u00e0m kh\u00f4ng x\u00e1c \u0111\u1ecbnh v\u00e0 ph\u1ea3i ghi gi\u1edbi h\u1ea1n hai ph\u00eda t\u1ea1i ti\u1ec7m c\u1eadn \u0111\u1ee9ng, gi\u1edbi h\u1ea1n t\u1ea1i v\u00f4 c\u1ef1c \u1ee9ng v\u1edbi ti\u1ec7m c\u1eadn ngang.<\/p>\n<h3>C\u00f3 c\u00f4ng c\u1ee5 n\u00e0o v\u1ebd b\u1ea3ng bi\u1ebfn thi\u00ean online kh\u00f4ng?<\/h3>\n<p>C\u00f3 m\u1ed9t s\u1ed1 c\u00f4ng c\u1ee5 v\u1ebd b\u1ea3ng bi\u1ebfn thi\u00ean online, nh\u01b0ng b\u1ea1n v\u1eabn n\u00ean t\u1ef1 l\u1eadp \u0111\u1ec3 hi\u1ec3u b\u00e0i; d\u00f9ng c\u00f4ng c\u1ee5 \u0111\u1ec3 ki\u1ec3m tra l\u1ea1i k\u1ebft qu\u1ea3 sau khi l\u00e0m.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean ch\u1ec9 c\u1ea7n nh\u1edb 4 b\u01b0\u1edbc: t\u1eadp x\u00e1c \u0111\u1ecbnh, \u0111\u1ea1o h\u00e0m v\u00e0 nghi\u1ec7m, gi\u1edbi h\u1ea1n, x\u00e9t d\u1ea5u v\u00e0 \u0111i\u1ec1n m\u0169i t\u00ean. H\u00e0m b\u1eadc hai l\u1eadp t\u1eeb t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh, h\u00e0m b\u1eadc ba v\u00e0 tr\u00f9ng ph\u01b0\u01a1ng d\u1ef1a v\u00e0o nghi\u1ec7m c\u1ee7a y&#8217;, c\u00f2n h\u00e0m ph\u00e2n th\u1ee9c c\u1ea7n th\u00eam ti\u1ec7m c\u1eadn. Luy\u1ec7n qua 4 v\u00ed d\u1ee5 tr\u00ean v\u00e0 \u0111\u1ecdc b\u1ea3ng \u0111\u1ec3 tr\u1ea3 l\u1eddi c\u00e1c c\u00e2u h\u1ecfi v\u1ec1 \u0111\u01a1n \u0111i\u1ec7u, c\u1ef1c tr\u1ecb, s\u1ed1 nghi\u1ec7m l\u00e0 b\u1ea1n \u0111\u1ee7 t\u1ef1 tin v\u1edbi d\u1ea1ng b\u00e0i n\u00e0y.<\/p>\n<p><strong>Xem th\u00eam:<\/strong><\/p>\n<ul>\n<li class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/so-huu-ti-la-gi\/\">S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec? S\u1ed1 v\u00f4 t\u1ec9 l\u00e0 g\u00ec? \u0110\u1eb7c tr\u01b0ng c\u1ee7a c\u00e1c s\u1ed1 trong To\u00e1n h\u1ecdc<\/a><\/li>\n<li class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-to-hop-chinh-hop\/\">B\u1ed9 c\u00f4ng th\u1ee9c Ho\u00e1n v\u1ecb \u2013 Ch\u1ec9nh h\u1ee3p \u2013 T\u1ed5 h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t trong To\u00e1n h\u1ecdc<\/a><\/li>\n<\/ul>\n<p><script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean g\u1ed3m m\u1ea5y b\u01b0\u1edbc?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"G\u1ed3m 4 b\u01b0\u1edbc: t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh, t\u00ednh \u0111\u1ea1o h\u00e0m v\u00e0 nghi\u1ec7m c\u1ee7a y', t\u00ednh gi\u1edbi h\u1ea1n, r\u1ed3i x\u00e9t d\u1ea5u y' \u0111\u1ec3 \u0111i\u1ec1n b\u1ea3ng v\u00e0 k\u1ebft lu\u1eadn.\"}},{\"@type\":\"Question\",\"name\":\"L\u1eadp b\u1ea3ng bi\u1ebfn thi\u00ean l\u1edbp 10 c\u00f3 c\u1ea7n \u0111\u1ea1o h\u00e0m kh\u00f4ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Kh\u00f4ng. V\u1edbi h\u00e0m b\u1eadc hai \u1edf l\u1edbp 10, b\u1ea1n l\u1eadp b\u1ea3ng d\u1ef1a v\u00e0o h\u1ec7 s\u1ed1 a v\u00e0 t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh I(\u2212b\/2a; \u2212\u0394\/4a).\"}},{\"@type\":\"Question\",\"name\":\"L\u00e0m sao bi\u1ebft m\u0169i t\u00ean \u0111i l\u00ean hay \u0111i xu\u1ed1ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Tr\u00ean kho\u1ea3ng y' mang d\u1ea5u +, m\u0169i t\u00ean \u0111i l\u00ean (h\u00e0m \u0111\u1ed3ng bi\u1ebfn); y' mang d\u1ea5u \u2212, m\u0169i t\u00ean \u0111i xu\u1ed1ng (h\u00e0m ngh\u1ecbch bi\u1ebfn).\"}},{\"@type\":\"Question\",\"name\":\"Khi n\u00e0o m\u1ed9t \u0111i\u1ec3m l\u00e0 c\u1ef1c tr\u1ecb trong b\u1ea3ng bi\u1ebfn thi\u00ean?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Khi y' \u0111\u1ed5i d\u1ea5u qua \u0111i\u1ec3m \u0111\u00f3: t\u1eeb + sang \u2212 l\u00e0 c\u1ef1c \u0111\u1ea1i, t\u1eeb \u2212 sang + l\u00e0 c\u1ef1c ti\u1ec3u. 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