导数五步法画函数图像10个函数示意图应用举例之一
\n\n
\n\n
1.函数y=(12x2+9)(4x2+14)的图像示意图：介绍函数的定义域、单调性、凸凹性、极限等性质及五点图表，并通过导数知识计算函数的单调和凸凹区间，简要画出示意图。
\n\n
2.函数y=(19x2+5)√(4x2+9)的主要性质及其图像：介绍函数的定义域、单调性、凸凹性、极限等性质，列举函数的五点图表，进一步画出函数的示意图。
\n\n
3.函数y=4√(x+80)^7图像画法及步骤：本文通过函数的定义、单调、凸凹性和极限等性质，介绍函数的主要性质及图像画法步骤。
\n\n
4.曲线x³+y³=2的主要性质及其图像示意图：介绍曲线方程的定义域、单调性、凸凹性等性质，同时用导数的知识求解函数的单调区间和凸凹区间，并简洁画出函数的图像示意图。
\n\n
5.√(x+4)+√(3y+5)=2的图像示意图：介绍曲线方程的定义域、单调性、凸凹性及极限等性质，同时用导数简洁画出函数的图像示意图。
\n\n
6.函数y=16x3+8x的图像示意图及主要性质：介绍函数的定义域、单调性、凸凹性、极限等性质，列举函数的五点图表，进一步画出函数的示意图。
\n\n
7.函数y=√(20x-87)^5图像画法及步骤：通过函数的定义、单调、凸凹和极限等性质， 并通过导数知识，介绍函数的主要性质及图像示意图画法步骤。
\n\n
8.函数y=log2(-2x+3)的图像示意图：介绍函数的定义域、单调性、凸凹性、极限等性质，列举函数的五点图表，简要画出函数的示意图。
\n\n
9.函数y=e^x(3x+4)的图像示意图：本文通过函数的定义、单调、凸凹性和极限等性质，介绍函数的主要性质及图像画法步骤。
\n\n
10.函数y=2^4x的图像示意图：介绍函数的定义域、单调性、凸凹性、极限等性质，列举函数的五点图表，进一步画出函数的示意图。
\n\n
\n\n
","gnid":"9758824ec7671aa4d","img_data":[{"flag":2,"img":[{"desc":"","height":925,"title":"","url":"https://p0.ssl.img.360kuai.com/t01a370aba0dc0184ae.jpg","width":1280},{"desc":"","height":925,"title":"","url":"https://p0.ssl.img.360kuai.com/t01fe729509bf6963a8.jpg","width":1280},{"desc":"","height":925,"title":"","url":"https://p0.ssl.img.360kuai.com/t01c644eeab94a0efe6.jpg","width":1280},{"desc":"","height":925,"title":"","url":"https://p0.ssl.img.360kuai.com/t013539215e0a83c2a4.jpg","width":1280},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t011ac510957e2c014e.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01b6300bde0321b12c.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t010ec62f9edc968eba.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t012ea8cadd7067c59a.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0135e6b9e5ad5f2723.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0101a95b931e2c6661.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0156869fd05f1b9bb9.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01eeb16f6ae9877b62.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01fd234f62dc83b806.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01a7177f0c14cf1b67.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01f3e9bcbfa66207be.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0111341fafd83e8b23.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01b12ae4529c0fc1a5.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01c2d414e70ce33022.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01a6435466e13d89c7.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0179a153481db89522.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t013f7979ab67311565.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t012871721b42a710c1.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t013b8fb94c7da143c9.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t015c6380a9e4dd5da4.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01c8edbb39b9d7fe87.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0122b1ab788e519a35.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01b446dfdddb35e4bf.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01651411583c303362.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0126094f1ca9ed1956.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t018fabf5214cdfc785.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t015b3f1e97b4dbe1ae.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01190830f3a32242fd.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01f1055028c526dd9d.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01e3ef63beab75c785.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t011dde9de6ce8a849b.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t019e8dbf2156e3031f.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t017d660aed63d492fa.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t017d660aed63d492fa.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0173f2a15f98505230.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0121e883d03506ad7f.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01fd20ffaf7942432d.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0174518a47ce9dd664.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t013e8e7b19fa695693.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0130fe2d9574be5db9.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0143c4b32aae3b438c.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01f74b752f697884fa.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0117c554a911c21419.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0141cfbe536892d640.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01d396d571728906e5.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01c87a38b737bd03fb.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t018eaaf25c81dbece5.jpg","width":"3509"}]}],"original":0,"pat":"pdc,art_src_0,fts0,sts0","powerby":"pika","pub_time":1711495200000,"pure":"","rawurl":"http://zm.news.so.com/7339c860ffebb01ebf215d79eb02f630","redirect":0,"rptid":"65e62da3ddba0208","rss_ext":[],"s":"t","src":"仁新数学","tag":[],"title":"导数五步法画函数图像10个函数示意图应用举例之一
苗贡狄2184函数y=2x+3/x+1的图像的对称中心的坐标是? 详细步骤 -
邱虽怪18129853342 ______ ∵函数f(x)=2x+3/x F(-x)=-2x-3/x=-f(x),∴为奇函数,关于原点对称将函数f(x)=2x+3/x图像垂直下移一个单位得函数y=2x+3/x-1的图像∴函数y=2x
苗贡狄2184一次函数y= - 2x+3的图象不经过第______象限. -
邱虽怪18129853342 ______[答案] ∵k=-2<0, ∴一次函数y=-2x+3的图象经过第二、四象限, ∵b=3>0, ∴一次函数y=-2x+3的图象与y轴的交点在x轴上方, ∴一次函数y=-2x+3的图象经过第一、二、四象限, 即一次函数y=-2x+3的图象不经过第三象限. 故答案为三.
苗贡狄2184已知二次函数y= - x2+2x+3(1)画出该函数的图像(2)指出此函数的开口方向,堆成周及定点坐标(3)求出它与X轴的交点坐标 -
邱虽怪18129853342 ______[答案] y=-x²+2x+3 y=-(x-1)²+4 y=-(x+1)(x-3) (2)∴a=-1<0 ∴开口方向向上; 定点坐标为(1,4) (3)与轴交点为(-1,0),(3,0)
苗贡狄2184如图,二次函数y= - x2+2x+3的图象与x轴交于A、B两点,与y轴交于点C,顶点为D,求△BCD的面积. -
邱虽怪18129853342 ______[答案] 依题意,可得y=-x2+2x+3=-(x-1)2+4. ∴顶点D(1,4). 令y=0,可得x=3或x=-1. ∴令x=0,可得y=3. ∴C(0,3). ∴OC=3, ∴直线DC的解析式为y=x+3. 设直线DE交x轴于E. ∴BE=6. ∴S△BCD=S△BED-S△BCE=3. ∴△BCD的面积为3.
苗贡狄2184函数y= - 2x+3的图象大致位置应是下图中的( )A. B. C. D. -
邱虽怪18129853342 ______[答案] y=-2x+3, ∵k=-2<0, ∴图象过第二、四象限,与y轴的交点坐标为(0,3),即与y轴的交点在x轴下方. 故选C.
苗贡狄2184已知点A是函数y=2x+3图像上一点,若A的横坐标为2,则A的纵坐标是( ) -
邱虽怪18129853342 ______ A的横坐标为2,纵坐标为7..
苗贡狄2184画出函数y= - 2x+3的图象,并利用图象解答下列问题,当x的值在 - 1/2≤x≤1的范围内变化,y的值在什么范围内变化若y的取值范围为1≤y≤5,则x的取值范围又是... -
邱虽怪18129853342 ______[答案] 由函数解析式可以知道,当y=1的时候,x=1,当y=5的时候x=-1 ,而我们可以从解析式中看出k<0,所以该函数呈下降趋势,所以x的取值范围应该为-1
苗贡狄2184做出y= - x^2+2x+3的图像,并求出函数的单调区间 -
邱虽怪18129853342 ______[答案] y=-x^2+2x+3=-(x-1)^2+4 开口向下 单调增区间(-∝,1) 单调减区间(1,+∝)
苗贡狄2184函数y= - x²+2x+3的图像的顶点坐标是 -
邱虽怪18129853342 ______ y= -x² + 2x + 3= -x² + 2x - 1 + 4= -(x - 1)² + 4 所以顶点坐标 (1 , 4 )
苗贡狄2184已知二次函数y=x2—2x+3,(1)判断该函数的图像与x轴的公共点的个数 (2)把该函数的图像 -
邱虽怪18129853342 ______ (1)y=x^2-2x+3=(x-1)^2+2 由于(x-1)^2≥0 所以 y>0,即该函数图像与x轴的公共点为0 (2)y=(x-1)^2+2,令Y=y-2,X=x-1,该函数即可转换为Y=X^2,所以该函数图像为抛物线曲线,函数图像为y=x^2右移1个单位上移2个单位.