How do you find the asymptotes for f(x)=(x^2-2x)/(x^2-5x+4)?
1 Answer
Feb 19, 2016
vertical asymptotes at x = 1 and x = 4
horizontal asymptote at y = 1
Explanation:
Vertical asymptotes occur when the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.
solve
x^2 - 5x + 4 = 0
factoring gives:
(x-1)(x-4) = 0rArr x = 1 , x = 4 Horizontal asymptotes occur as
lim_(x→±∞) f(x) → 0 If the degree of the numerator and denominator are equal , then the equation can be found by taking the ratio of leading coefficients.
Here they are both of degree 2 hence:
here is the graph of the function to illustrate these.
graph{(x^2-2x)/(x^2-5x+4) [-20, 20, -10, 10]}