Question

下圖是指數(shù)函數(shù):①y=a^x；②y=b^x；③y=c^x；④y=d^x的圖象,則a、b、c、d與1的大小關(guān)系是

A.a<b<1<c<d                                                  B.b<a<1<d<c

C.1<a<b<c<d                                                  D.a<b<1<d<c

Answer 1

解法一:在①②中底數(shù)小于1且大于零,在y軸右邊,底數(shù)越小,圖象越靠近x軸,故有b<a.在③④中底數(shù)大于1,底數(shù)越大圖象越靠近y軸,故有d<c.∴選B.

解法二:設(shè)x=1與①②③④的圖象分別交于點(diǎn)A、B、C、D,則其坐標(biāo)依次為(1,a)、(1,b)、(1,c)、(1,d),由圖象觀察可得c>d>1>a>b.故選B.

答案:B

點(diǎn)評(píng):當(dāng)指數(shù)函數(shù)底數(shù)大于1時(shí),圖象上升,且當(dāng)?shù)讛?shù)越大,圖象向上越靠近于y軸,當(dāng)?shù)讛?shù)大于0小于1時(shí),圖象下降,底數(shù)越小,圖象向下越靠近于x軸,簡(jiǎn)稱x>0時(shí),底大圖象高.