2022年函数的图象导学案 .pdf

学习好资料欢迎下载课题:1912 函数的图象导学案姓名:班级:【学习目标】：1了解函数图象的意义，能从函数图象中分析和获取信息2能分析和研究问题中的数量关系，培养读图能力3掌握用描点法画函数图象的基本步骤，能结合图象说出函数的性质.4体验数与形的内在联系，感受函数图象的简洁美学习重点：函数图象的意义及能从图象中读出有关的信息;掌握用描点法画函数图象的基本步骤学习难点：用数形结合的思想研究函数能结合图象说出函数的性质一、新课引入下面的图象反映的过程是：小明从家去菜地浇水，又去玉米地锄草，然后回家，其中x表示时间，y表示小明离他家的距离小明家、菜地、玉米在同一直线上根据图象回答下列问题：（1）菜地离小明家多远？小明从家到菜地用了多少时间？（2）小明给菜地浇水用了多少时间？（3）菜地离玉米地多远？小明从菜地到玉米地用了多少时间？（4）小明给玉米地锄草用了多少时间？（5）玉米地离小明家多远？小明从玉米地走回家的平均速度是多少？二、课堂探究探究 1 正方形的面积y与边长x的函数关系式为y=，其中自变量x的取值范围是_计算并填写下表：x0 0.5 1 1.5 2 2.5 3 3.5 4 y（x，y）回答或操作：（1）如果以自变量x的一个确定的值与它对应的唯一的函数值y，分别作为横坐标，纵坐标，是否确定一个点（x，y）呢？（2）自变量x的值有多少个？表示x 与y的对应关系的点有多少个？学习好资料欢迎下载（3）在下边的直角坐标系中，请将上面表格中的各对数值所对应的点画出，然后连接这些点，所得的曲线上的每一点都代表自变量x的值与y值的一种对应，例如点（2，4）表示当x=2 时，y=4.（4）因为x=0 不在x的取值范围内，所以点（0，0）不在图象上，所以用空心圈表示点（0，0）若该点在图象上，则应该用实心点表示归纳小结：1、一般地，对于一个函数，如果把分别作为点的_、，那么坐标平面内由这些点组成的图形，就是这个函数的_.2、归纳描点法画函数图象的一般步骤：（1）_（表中给出一些自变量的值及其对应的函数值）（2）_（在直角坐标系中，以自变量的值为横坐标，对应的函数值为纵坐标，描出表格中数值对应的各点）；（3）_（按照横坐标由小到大的顺序把所描的各点用平滑的曲线连接起来）探究 2(1)1xy注意：在1xy中，自变量x的取值为全体实数；x3 2 1 0 1 2 3 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ZE8R4D1U10H7学习好资料欢迎下载（2）xy6)0(x注意：在xy6中，自变量x的取值为0 x(2)观察图象：(1)上述图象(1)从左到右（填上升或下降），即当自变量x由小变大时，函数值y随之变(2)上述图象(2)从左到右（填上升或下降），即当自变量x由小变大时，函数值y随之变思考：（1）点（1，1）在函数1xy的图象上吗？（2）点（2，3）在函数xy6)0(x的图象上吗？课堂总结1、一般地，对于一个函数，如果把分别作为点的_、，那么坐标平面内由这些点组成的图形，就是这个函数的_.2、描点法画函数图象的一般步骤：_ _ _.3、注意事项（1）自变量的取值不宜过大或过小，尽可能取整数.（2）连线时，必须按照横坐标从小到大（或从大到小）进行.（3）列表中的自变量、函数值分别对应着该点的横、纵坐标，防止出现横、纵坐标颠倒的错误.【拓展延伸】小亮早晨从家骑车到学校，先上坡后下坡，行程情况如图所示若返回时上坡、下坡的速度仍与上学时相同，请根据图象，求出小明从学校骑车回家所用的时间xy（x，y）文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 ZE8R4D1U10H7文档编码:CQ3Y3C8H8P1 HQ5H5Y4F1U9 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