思考:對(duì)于函數(shù).當(dāng)自變量取一對(duì)相反數(shù)時(shí).函數(shù)值也得到一對(duì)相反數(shù).則 查看更多

 

題目列表(包括答案和解析)

閱讀下列材料再回答問(wèn)題:
對(duì)于函數(shù)y=x2,當(dāng)x=1時(shí),y=1,當(dāng)x=-1時(shí),y=1;當(dāng)x=2時(shí),y=4,當(dāng)x=-2時(shí),y=4;…
而點(diǎn)(1,1)與(-1,1),(2,4)與(-2,4),…,都關(guān)于y軸對(duì)稱(chēng).顯然,如果點(diǎn)(x0,y0)在函數(shù)y=x2的圖象上,那么,它關(guān)于y軸對(duì)稱(chēng)的點(diǎn)(-x0,y0)也在函數(shù)y=x2的圖象上,這時(shí),我們說(shuō)函數(shù)y=x2關(guān)于y軸對(duì)稱(chēng).
一般地,如果對(duì)于一個(gè)函數(shù),當(dāng)自變量x在允許范圍內(nèi)取值時(shí),若x=x0和x=-x0時(shí),函數(shù)值都相等,我們說(shuō)函數(shù)的圖象關(guān)于y軸對(duì)稱(chēng).
問(wèn)題:
(1)對(duì)于函數(shù)y=x3,當(dāng)自變量x取一對(duì)相反數(shù)時(shí),函數(shù)值也得到一對(duì)相反數(shù),則函數(shù)y=x3的圖象關(guān)于
原點(diǎn)
原點(diǎn)
對(duì)稱(chēng).(“x軸”、“y軸”或“原點(diǎn)”).
(2)下列函數(shù):①y=x3+2x;②y=2x4+4x2;③y=x+
1
x
;④y=-x-2 中,其圖象關(guān)于y軸對(duì)稱(chēng)的有
②④
②④
,關(guān)于原點(diǎn)對(duì)稱(chēng)的有
①③
①③
(只填序號(hào)).
(3)請(qǐng)你寫(xiě)出一個(gè)我們學(xué)過(guò)的函數(shù)關(guān)系式
y=
k
x
(k≠0)
y=
k
x
(k≠0)
,其圖象關(guān)于直線(xiàn)y=x對(duì)稱(chēng).

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閱讀下列材料再回答問(wèn)題:
對(duì)于函數(shù)y=x2,當(dāng)x=1時(shí),y=1,當(dāng)x=-1時(shí),y=1;當(dāng)x=2時(shí),y=4,當(dāng)x=-2時(shí),y=4;…
而點(diǎn)(1,1)與(-1,1),(2,4)與(-2,4),…,都關(guān)于y軸對(duì)稱(chēng).顯然,如果點(diǎn)(x0,y0)在函數(shù)y=x2的圖象上,那么,它關(guān)于y軸對(duì)稱(chēng)的點(diǎn)(-x0,y0)也在函數(shù)y=x2的圖象上,這時(shí),我們說(shuō)函數(shù)y=x2關(guān)于y軸對(duì)稱(chēng).
一般地,如果對(duì)于一個(gè)函數(shù),當(dāng)自變量x在允許范圍內(nèi)取值時(shí),若x=x0和x=-x0時(shí),函數(shù)值都相等,我們說(shuō)函數(shù)的圖象關(guān)于y軸對(duì)稱(chēng).
問(wèn)題:
(1)對(duì)于函數(shù)y=x3,當(dāng)自變量x取一對(duì)相反數(shù)時(shí),函數(shù)值也得到一對(duì)相反數(shù),則函數(shù)y=x3的圖象關(guān)于______對(duì)稱(chēng).(“x軸”、“y軸”或“原點(diǎn)”).
(2)下列函數(shù):①y=x3+2x;②y=2x4+4x2;③數(shù)學(xué)公式;④y=-x-2 中,其圖象關(guān)于y軸對(duì)稱(chēng)的有______,關(guān)于原點(diǎn)對(duì)稱(chēng)的有______(只填序號(hào)).
(3)請(qǐng)你寫(xiě)出一個(gè)我們學(xué)過(guò)的函數(shù)關(guān)系式______,其圖象關(guān)于直線(xiàn)y=x對(duì)稱(chēng).

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已知二次函數(shù),當(dāng)自變量取兩個(gè)不同的值時(shí)函數(shù)值相等,則當(dāng)自變量時(shí)函數(shù)值與(         )

A.時(shí)的函數(shù)值相等                 B.時(shí)的函數(shù)值相等

C.時(shí)的函數(shù)值相等                 D.時(shí)的函數(shù)值相等

 

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已知二次函數(shù),當(dāng)自變量時(shí),對(duì)應(yīng)的函數(shù)值大于0,當(dāng)自變量分別取,時(shí)對(duì)應(yīng)的函數(shù)值、,則,滿(mǎn)足  

A.>0,>0B.<0,<0 C.<0,>0D.>0,<0

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已知二次函數(shù),當(dāng)自變量時(shí),對(duì)應(yīng)的函數(shù)值大于0,當(dāng)自變量分別取,時(shí)對(duì)應(yīng)的函數(shù)值、,則,滿(mǎn)足  

A.>0,>0      B.<0,<0      C.<0,>0      D.>0,<0

 

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