答案A
6已知一次函数y=2x+a与y=-x+b的图象都经过A(-2,0),且与y轴分别交于B,C两点,则△ABC的面积为( )
A.4 B.5 C.6 D.7
解析由已知得0=2×(-2)+a,
即a=4.
同理-(-2)+b=0,即b=-2.
故两个一次函数分别是y=2x+4与y=-x-2.
与y轴交于点B(0,4),C(0,-2),故S△ABC=1/2×6×2=6.
答案C
7若函数y=ax+1在[1,2]上的最大值与最小值的差为2,则实数a的值是( )
A.2 B.-2 C.2或-2 D.0
解析显然有a≠0,当a>0时,y=ax+1在[1,2]上单调递增,
故(2a+1)-(a+1)=2,解得a=2;
当a<0时,y=ax+1在[1,2]上单调递减,
故(a+1)-(2a+1)=2,解得a=-2.
综上可知,a=2或-2.
答案C
8若f(x)是一次函数,且f(f(x))=4x-1,则f(x)= .
解析设f(x)=kx+b(k≠0),则k(kx+b)+b=4x-1,
即k2x+kb+b=4x-1,
即{■(k^2=4"," @kb+b="-" 1"," )┤解得{■(k=2"," @b="-" 1/3 "," )┤或{■(k="-" 2"," @b=1"." )┤
故f(x)=2x-1/3或f(x)=-2x+1.
答案2x-1/3或-2x+1
9若函数y=ax-2与y=bx+3的图象与x轴交于同一点,则a/b等于 .
解析设交点为(m,0),
所以{■(am"-" 2=0"," @bm+3=0"," )┤即{■(am=2"," @bm="-" 3"." )┤
所以a/b=-2/3.
答案-2/3