posted by Hyde on .
For the function y= (ax+b)/(cx+d) write the intervals where the function is increasing and intervals where it is decreasing.
X intercept= -b/a
Y intercept= b/d
Vertical asymptote: x=-d/c
Horozontal asymptote: a/c
your answeres are correct so far.
for the increasing/decreasing part,
I got (-c((ax+b) + a(cx+d))/(cx+d)^2
= (ad - bc)/(cx + d)^2
since the denominator is always ≥ 0
we only have to look at the top
for the function to increase , dy/dx > 0
ad - bc > 0
for the function to decrease,
ad - bc < 0