Question

Need help in finding all vertical, horizontal, and slant asymptotes, x- and y-intercepts, and symmetries of f(x)=(x-3)/(x-4)

Answer 1

using quotient rule,
dy/dx - (x-4 - (x-3))/(x-4)^2

VA: x=4
HA: y=1
so slants

for y-intercept, let x = 0, then y =3/4
(0, 3/4)
for x-intercept , let y = 0

verification:
http://www.wolframalpha.com/input/?i=plot+y+%3D%28x-3%29%2F%28x-4%29
(x-3)/(x-4) = 0
x = 3 ---> x-intercept is (3, 0)

Answer 2

thank you!