中職數(shù)學(xué)課件3.3 函數(shù)的單調(diào)性

3.3函數(shù)的單調(diào)性【復(fù)習(xí)目標(biāo)】1.理解和掌握函數(shù)單調(diào)性的定義.2.掌握判斷和證明函數(shù)單調(diào)性的方法.3.能利用函數(shù)的單調(diào)性解決簡單問題.【知識(shí)回顧】1.函數(shù)單調(diào)性的定義(1)對于函數(shù)f(x),在給定區(qū)間上的任意兩個(gè)自變量x1,x2,當(dāng)x1<x2都有f(x1)<f(x2),那么就說y=f(x)在這個(gè)區(qū)間上是增函數(shù).(2)對于函數(shù)f(x),在給定區(qū)間上的任意兩個(gè)自變量x1,x2,當(dāng)x1<x2都有f(x1)>f(x2),那么就說y=f(x)在這個(gè)區(qū)間上是減函數(shù).【例題精解】【答案】(1)k>0;(2)m>0;(3)增【例2】試求a的取值范圍.(1)loga8<loga2 (2)log0.3a>log0.35【解】(1)考查y=logax(a>0且a≠1)

∵8>2且loga8<loga2∴函數(shù)y=logax在(0,+∞)是減函數(shù)∴a的取值范圍是0<a<1.(2)函數(shù)y=log0.3x在(0,+∞)是減函數(shù)∵log0.3a>log0.35

∴a<5又∵a為真數(shù)∴a的取值范圍是0<a<5【例3】若函數(shù)y=x2+mx+9在區(qū)間(-∞,3]單調(diào)遞減,在區(qū)間[3,+∞)單調(diào)遞增,試求m的值.【同步訓(xùn)練】【答案】C一、選擇題1.下列命題正確的是 (

) A.函數(shù)y=kx-1,當(dāng)k>0時(shí),在區(qū)間(-∞,+∞)上是減函數(shù) B.函數(shù)y=kx-1,當(dāng)k<0時(shí),在區(qū)間(-∞,+∞)上是增函數(shù) C.函數(shù)y=kx-1,當(dāng)k>0時(shí),在區(qū)間(-∞,+∞)上是增函數(shù) D.函數(shù)y=kx-1,當(dāng)k>0時(shí),在區(qū)間[0,+∞)上是減函數(shù)【答案】C2.函數(shù)f(x)=-3x+1 (

) A.在(0,+∞)上是增函數(shù) B.在(-∞,0)上是增函數(shù) C.在(-∞,+∞)上是減函數(shù) D.在(-∞,+∞)上是增函數(shù)【答案】C【答案】A4.函數(shù)f(x)=-5x2 (

) A.在(-∞,0)上是增函數(shù) B.在(0,+∞)上是增函數(shù) C.在(-∞,+∞)上是減函數(shù) D.在(-∞,+∞)上是增函數(shù)【答案】C【答案】A6.函數(shù)y=log2x (

) A.在(0,+∞)上是增函數(shù) B.在[0,+∞)上是增函數(shù) C.在(0,+∞)上是減函數(shù) D.在[0,+∞)上是減函數(shù)【答案】D【答案】B8.一次函數(shù)y=kx+b在(-∞,+∞)上是單調(diào)遞減函數(shù),且圖象不過第三象限(

) A.k>0,b≠0 B.k<0,b≥0 C.k<0,b≠0 D.k>0,b<0【答案】D【答案】D10.函數(shù)①y=2(x-2)2+4;②y=2(x+2)2-3;③y=x2-4x;④y=x2+4x在區(qū)間[-2,+∞)上是增函數(shù)的有 (

) A.①和② B.③和④ C.①和③ D.②和④[0,+∞)(-∞,0](2)、(3)36三、解答題17.