Question

y=(ax+b)/(cx+d)值域

Answer 1

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