(1)当y=0时,kx+k=0,解得:x=-1,故A点坐标为:(-1,0);(2)∵点B的坐标为(4,0),∴AB=5,作MN⊥x轴于点N,∵S△ABM= 1 2 MN×AB=10,AB=5,∴解得:MN=4,∵AM=5,根据勾股定理求出:AN= 52?42 =3,∴ON=2,∴M点的坐标为(2,4),∴k=xy=8,∴双曲线的函数表达式为:y= 8 x .