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第一PPT > PPT課件 > 數(shù)學(xué)課件 > 人教高中數(shù)學(xué)A版必修一 > 《對(duì)數(shù)函數(shù)》指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT(第1課時(shí)對(duì)數(shù)函數(shù)的概念、圖象及性質(zhì))

《對(duì)數(shù)函數(shù)》指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT(第1課時(shí)對(duì)數(shù)函數(shù)的概念、圖象及性質(zhì))

《對(duì)數(shù)函數(shù)》指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT(第1課時(shí)對(duì)數(shù)函數(shù)的概念、圖象及性質(zhì)) 詳細(xì)介紹:

《對(duì)數(shù)函數(shù)》指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT(第1課時(shí)對(duì)數(shù)函數(shù)的概念、圖象及性質(zhì))《對(duì)數(shù)函數(shù)》指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT(第1課時(shí)對(duì)數(shù)函數(shù)的概念、圖象及性質(zhì))《對(duì)數(shù)函數(shù)》指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT(第1課時(shí)對(duì)數(shù)函數(shù)的概念、圖象及性質(zhì))《對(duì)數(shù)函數(shù)》指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT(第1課時(shí)對(duì)數(shù)函數(shù)的概念、圖象及性質(zhì))《對(duì)數(shù)函數(shù)》指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT(第1課時(shí)對(duì)數(shù)函數(shù)的概念、圖象及性質(zhì))

《對(duì)數(shù)函數(shù)》指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT(第1課時(shí)對(duì)數(shù)函數(shù)的概念、圖象及性質(zhì))

第一部分內(nèi)容:學(xué)習(xí)目標(biāo)

理解對(duì)數(shù)函數(shù)的概念,會(huì)判斷對(duì)數(shù)函數(shù)

初步掌握對(duì)數(shù)函數(shù)的圖象和性質(zhì)

能利用對(duì)數(shù)函數(shù)的性質(zhì)解決與之有關(guān)的定義域問題

... ... ...

指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT,第二部分內(nèi)容:自主學(xué)習(xí)

問題導(dǎo)學(xué)

預(yù)習(xí)教材P130-P135,并思考以下問題:

1.對(duì)數(shù)函數(shù)的概念是什么?它的解析式具有什么特點(diǎn)?

2.對(duì)數(shù)函數(shù)的圖象是什么形狀?你能畫出y=log2x與y=log12x的圖象嗎?

3.通過對(duì)數(shù)函數(shù)的圖象,你能觀察到函數(shù)的哪些性質(zhì)?

新知初探

1.對(duì)數(shù)函數(shù)的概念

一般地,函數(shù)y=____________________叫做對(duì)數(shù)函數(shù),其中____是自變量,函數(shù)的定義域是__________.

■名師點(diǎn)撥

在對(duì)數(shù)函數(shù)的定義表達(dá)式y(tǒng)=logax(a>0,且a≠1)中,logax前邊的系數(shù)必須是1,自變量x在真數(shù)的位置上,否則就不是對(duì)數(shù)函數(shù).

2.對(duì)數(shù)函數(shù)的圖象及性質(zhì)

■名師點(diǎn)撥

底數(shù)a與1的大小關(guān)系決定了對(duì)數(shù)函數(shù)圖象的“升降”:當(dāng)a>1時(shí),對(duì)數(shù)函數(shù)的圖象“上升”;當(dāng)0<a<1時(shí),對(duì)數(shù)函數(shù)的圖象“下降”.

3.反函數(shù)

指數(shù)函數(shù)y=ax(a>0,且a≠1)和對(duì)數(shù)函數(shù)y=logax(a>0,且a≠1)互為反函數(shù).兩者的_______和_______正好互換. 

自我檢測

判斷正誤(正確的打“√”,錯(cuò)誤的打“×”)

(1)y=log2x2與y=logx3都是對(duì)數(shù)函數(shù).(  )

(2)對(duì)數(shù)函數(shù)的定義域、值域都是R.(  )

(3)對(duì)數(shù)函數(shù)的圖象一定在y軸右側(cè).(  )

(4)函數(shù)y=log2x與y=2x互為反函數(shù).(  )

下列函數(shù)是對(duì)數(shù)函數(shù)的是(  )

A.y=lnx B.y=ln(x+1)

C.y=logxe  D.y=logxx

函數(shù)f(x)=lg(3x)-2-x的定義域是(  )

A.(0,2) B.[0,2]

C.[0,2) D.(0,2]

... ... ...

指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT,第三部分內(nèi)容:講練互動(dòng)

對(duì)數(shù)函數(shù)的概念

下列函數(shù)中,哪些是對(duì)數(shù)函數(shù)?

(1)y=logax(a>0,且a≠1);

(2)y=log2x+2;

(3)y=8log2(x+1);

(4)y=logx6(x>0,且x≠1);

(5)y=log6x.

【解】(1)中真數(shù)不是自變量x,不是對(duì)數(shù)函數(shù).(2)中對(duì)數(shù)式后加2,所以不是對(duì)數(shù)函數(shù).(3)中真數(shù)為x+1,不是x,系數(shù)不為1,故不是對(duì)數(shù)函數(shù).(4)中底數(shù)是自變量x,而非常數(shù),所以不是對(duì)數(shù)函數(shù).(5)中底數(shù)是6,真數(shù)為x,系數(shù)為1,符合對(duì)數(shù)函數(shù)的定義,故是對(duì)數(shù)函數(shù).

與對(duì)數(shù)函數(shù)有關(guān)的定義域問題

求下列函數(shù)的定義域:

(1)y=1log2(x-1);

(2)y=log2(16-4x);

(3)y=log(x-1)(3-x).

規(guī)律方法

(1)求與對(duì)數(shù)函數(shù)有關(guān)的函數(shù)定義域時(shí)應(yīng)遵循的原則

①分母不能為0;

②根指數(shù)為偶數(shù)時(shí),被開方數(shù)非負(fù);

③對(duì)數(shù)的真數(shù)大于0,底數(shù)大于0且不為1.

(2)求函數(shù)定義域的步驟

①列出使函數(shù)有意義的不等式(組);

②化簡并解出自變量的取值范圍;

③確定函數(shù)的定義域. 

... ... ...

指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT,第四部分內(nèi)容:達(dá)標(biāo)反饋

1.對(duì)數(shù)函數(shù)的圖象過點(diǎn)M(16,4),則此對(duì)數(shù)函數(shù)的解析式為(  )

A.y=log4x  B.y=log14x

C.y=log12x    D.y=log2x

解析:選D.由于對(duì)數(shù)函數(shù)的圖象過點(diǎn)M(16,4),所以4=loga16,得a=2.所以對(duì)數(shù)函數(shù)的解析式為y=log2x,故選D.

2.已知函數(shù)f(x)=loga(x-1)+4(a>0,且a≠1)的圖象恒過定點(diǎn)Q,則Q點(diǎn)坐標(biāo)是(  )

A.(0,5)   B.(1,4)     C.(2,4)   D.(2,5)

3.若函數(shù)y=loga(x+a)(a>0且a≠1)的圖象過點(diǎn)(-1,0).

(1)求a的值;

(2)求函數(shù)的定義域.

... ... ...

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