Question

一次函数y=ax+b的图像与反比例函数y=k/x的图像交于A,B两点,AC⊥x轴,S△AOC=4,点A的横坐标与点B的纵

Answer 1

(1) A(a,k/a),a < 0,k < 0

S△AOC=4 = (1/2)OC*CA = (1/2)(-a)(k/a) = -k/2

k = -8

y = -8/x

A(-2,4):4 = -2a + b (i)

B(4,-2):-2 = 4a + b (ii)

由(i)(ii):a = -1,b = 2

y = -x + 2

(2) x < -2或0 < x < 4

(3)

y = -x + 2

y = 0,x = 2

一次函数与x轴交于D(2,0)

△AOB的面积 = △AOD的面积 + △BOD的面积

= (1/2)OD*CA + (1/2)OD*|B的纵坐标|

= (1/2)*2*4 + (1/2)*2*|-2|

= 6