Find The Vertical And Horizontal Asymptotes Of The Graphs Of The Following:?

Question

1) y = x^3 / x^2 + 3x - 10
2) y = x^3 + 1 / x^3 + x
3) y = x - 9 / root(4x^2 + 3x + 2)
4) y = 1 / 1 + e^-x

Answer 1

1) Vertical asymptotes at x = -5 and x=2 because denominator = (x+5)(x -2) goes to 0 at x = -5 and 2.

2. vertical asymptote at x =0 and horizotal asymptote at y=1.

3) Horizotal asymptote at y = -.5

4) Horizontal asymptote at x-axis if x<0,
Horizontal asymptote of y=1 if x>0
At x= 0 y = .5

Answer 2

1) x^3 / (x+5)(x-2) There are asymptotes at the line x=-5 and another at x=2.
2) Asymptote at x=0 QED.
3) No real solutions
4) No Asymptotes

Answer 3

stick em in a graphing calculator.

Answer 4

http://www.mathworld.wolfram.com