Question

函數(shù)f(x)=2x-sinx的零點(diǎn)個(gè)數(shù)為

A．1

B．2

C．3

D．4

Answer 1

A

試題分析：解：因?yàn)楹瘮?shù)的零點(diǎn)個(gè)數(shù)就是找對(duì)應(yīng)兩個(gè)函數(shù)的圖象的交點(diǎn)個(gè)數(shù)．在同一坐標(biāo)系內(nèi)畫(huà)出函數(shù)y=sinx與y=2x的圖象，由圖得交點(diǎn)1個(gè)，故函數(shù)f（x）=sinx-2x的零點(diǎn)的個(gè)數(shù)是1．故選A．
點(diǎn)評(píng)：本題考查函數(shù)零點(diǎn)個(gè)數(shù)的判斷和數(shù)形結(jié)合思想的應(yīng)用．在判斷函數(shù)零點(diǎn)個(gè)數(shù)時(shí)，常轉(zhuǎn)化為對(duì)應(yīng)方程的根，利用根的個(gè)數(shù)來(lái)得結(jié)論或轉(zhuǎn)化為對(duì)應(yīng)兩個(gè)函數(shù)的圖象的交點(diǎn)，利用兩個(gè)函數(shù)的圖象的交點(diǎn)個(gè)數(shù)來(lái)判斷．