函数及其图象单元测试题3

函数及其图象单元测试题3

一、耐心填一填：(每空3分,共30分)

1.函数

的自变量x 的取值范围是_______. 2.已知点P 在第四象限,且到x 轴距离为3,到y 轴距离为4,则P 点坐标为_____. 3.有一面积为60的梯形,其上底长是下底长的

13,若下底长为x,高为y,则y 与x 的函数关系式为________.

4.函数12

x - 的自变量x 取值范围是_______. 5.圆心都在x 轴上两圆相交于A 、B 两点,已知A 点坐标为A(-3,4),则B 点坐标为_______.

6.已知一次函数的图象与双曲线y=-2x

交于点(-1,m),且过点(0,1),那么这个一次函数的解析式为________.

7.点A(1,m)在函数y=2x 的图象上,则点A 关于y 轴的对称点坐标为________.

8.已知y 与(2x+1)成反比例,且当x=1时,y=2,那么当x=-1时y=_______.

9.已知一次函数y=2x-k 的图象与反比例函数y=

5k x + 的图象相交,其中一个交点纵坐标为-4,则k=________.

10.如图,面积为3的矩形OABC 的一个顶点B 在反比例函数y=k x

的图象上,另三个顶点在坐标轴上,则k=__________.

二、精心选一选：(每题4分,共36分)

11.如图,OA 、BA 分别表示甲、乙两名学生运动的一次函数图象,图中s 和t 分别表示运动路程

和时间,根据图象判断快者的速度比慢者的速度每秒快 ( )

A.2.5米

B.2米

C.1.5米

D.1米

12.若点P(1-m,m)在第二象限,则下列关系式正确的是( )

A.0

B.m<0

C.m>0

D.m>1

13.已知一次函数y=k 1x+b,y 随x 的增大而减小,且b>0;反比例

函数y=2k x 中的k 2与k 1的值相等,则它们在同一坐标系中的图象只可能是( )

14.已知圆柱体的侧面积为80πcm 2

,若圆柱底面半径为r(cm),高线长为h(cm),则h 关于r 的函数的图象大致是( )

15.下列函数中,图象大致为如图的是( )

A.y=1x (x<0)

B.y=1x

(x>0) C.y=-1x (x>0) D.y=-1x

(x<0) 16.某天早晨,小强从家里出发,以v 1的速度前往学校,途中在一饮食店吃早点,之后,以v 2的速度向学校行进,已知v 1>v 2, 下面的图象中表示小强从家到学校的时间t(分钟)与程程s(千米)之间的关系是( )

17.反比例函数y=3k x

+ 的图象在每个象限内的函数值y 随自变量x 的增大而增大, 那么k 的取值范围是( )

A.k ≤-3

B.k ≥-3

C.k>-3

D.k<-3

18.已知反比例函数y=k x

(k>0),当x=-1.2,-3时对应的函数值分别为y 1,y 2,y 3,则y1,y2,y3的大小关系是( )

A.y 3>y 2>y 1

B.y 2>y 3>y 1；

C.y 1>y 2>y 3

D.y 2>y 1>y 3

19.如图,函数y=x 与y=mx(m>0,且m 为常数)与反比例函数y=k x

(k>0)的图象分别交于点A 和C,若Rt △AOB 与Rt △COD 的面积分别为S 1,S 2,则S 1与S 2的大小关系是( )

A.S 1>S 2

B.S 1=S 2；

C.S 1

D.不能确定

三、细心解一解：(每题10分,共30分)

20.已知反比例函数y=a x

和一次函数y=kx+b 的图象都经 过(2,-1),(1,c)两点, 求这两个函数的解析式.

21.已知直线y=2x+1。

(1)求已知直线与y轴交点A的坐标. (2)若直线y=kx+b与已知直线关于y轴对称,求k与b.

22.汽车的油箱中的余油量Q(升)与它行驶的时间t(小时) 之间是一次函数关系,某天该汽车外

出,刚开始行驶时,油箱中有油60升,行驶了4小时后,发现已耗油20升.

(1)求:油箱中的余油Q与行驶时间t的函数关系式.

(2)求:这个实际问题中时间t的取值范围,并在直角坐标中作出该函数图象.

(3)如果汽车每小时行驶40千米,那么汽车行驶多远必须加油?

四、用心想一想：(10分)

23.某衡器厂生产的RGZ-120型体重秤,最大称重120千克, 你在体检时可看到显示盘,已知,指

针顺时针旋转角x(度)

(1)根据表格中的数据在直角坐标系中描出相应的点,顺次连接各点后, 你发现这些点在哪一种图形上?合情猜想符合这个图形的函数解析式;

(2)验证这些点的坐标是否满足函数解析式,归纳你的结论(写出自变量x的取值范围)

(3)当指针旋转到158.4度的位置时,利用解析式求出此时体重.

五、创新练习：(14分)

24.阅读函数图象,并根据你所获得的信息回答问题:

(1)折线OAB表示某个实际问题的函数图象, 请你编写一道符合该图意义的应用题;

(2)根据你给出的应用题分别指出x轴,y轴所表示的意义,并写出A、B 两点坐标;

(3)求出图象AB的函数解析式,并注明自变量x的取值范围.

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