添加关联题

题库0.3/Problems.json

@@ -3408,7 +3408,8 @@
         ],
         "same": [],
         "related": [
-            "030046"
+            "030046",
+            "022911"
         ],
         "remark": "",
         "space": "4em",
@@ -609924,6 +609925,38 @@
         "space": "4em",
         "unrelated": []
     },
+    "022911": {
+        "id": "022911",
+        "content": "作出函数$y=(x^2-1)^2-1$的大致图像, 写出它所有的单调区间, 并在其中一个单调区间上证明单调性.",
+        "objs": [
+            "K0219001B",
+            "K0219003B",
+            "K0220001B"
+        ],
+        "tags": [
+            "第二单元",
+            "2023届高三-寒假作业-中档题",
+            "2023届高三-第一轮复习讲义-08-函数的单调性"
+        ],
+        "genre": "4em",
+        "ans": "在$(-\\infty,-1]$及$[0,1]$上分别严格增, 在$[-1,0]$及$[1,+\\infty)$上分别严格减; 证明略; 图像如下:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1.7:1.7] plot (\\x,{pow((\\x * \\x -1),2)-1});\n\\end{tikzpicture}\n\\end{center}",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "教材复习题-20231204修改",
+        "edit": [
+            "20220624\t王伟叶, 余利成",
+            "20231204\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "030046",
+            "000092"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",