y=(ax+b)/(cx+d)值域

2个回答

  • 首先不能全为0,否则y无意义正.

    (1) a = 0,b = 0 (但c,d不均为0),y = 0

    (2) a = 0,b ≠ 0,c = 0,d ≠ 0,y = b/d

    (3) a = 0,b ≠ 0,c ≠ 0

    y = b/(cx + d) = (b/c)/(x + d/c)

    此由y = (b/c)/x向左平移d/c得到,值域为y ≠ 0

    (4) a ≠ 0,c ≠ 0,b = 0,d≠ 0

    y = a/c - (d/c)/(x + d/a)

    此由y = -(d/c)/x向上平移a/c,向左平移d/a得到,值域为y ≠ a/c

    (5) a ≠ 0,c ≠ 0,b ≠ 0,d = 0

    y = a/c + (b/c)/x

    此由y = (b/c)/x向上平移a/c得到,值域为y ≠ a/c

    (6)a,b,c,d均不为0

    y = a/c + [(bc-ad)/c²]/(x + d/c)

    此由y = [(bc-ad)/c²]/x向上平移a/c,向左平移d/c得到,值域为y ≠ a/c