How do you graph f(x)=(x-1)/(x+1) using holes, vertical and horizontal asymptotes, x and y intercepts?

1 Answer
marfre
Apr 25, 2017

Vertical asymptote: x = -1
Horizontal asymptote: y = 1
No holes, x-intercept (1, 0); y-intercept (0, -1)

Explanation:

Rational equation: f(x)=(N(x))/(D(x)) = (a_nx^n+...)/(b_mx^m+...)

Find x-intercepts N(x) = 0:
x-1 = 0; x = 1
x-intercept (1, 0)

Find y-intercepts Set x = 0:
f(0) = -1/1 = -1
y-intercept (0, -1)

Find holes:
Holes occur when factors can be cancelled because they are found both in the numerator and denominator. This does not occur in this problem.

Find the vertical asymptotes D(x) = 0:
Vertical asymptotes at x +1 = 0; x = -1

Find horizontal asymptotes When m=n, y = a_n/b_m:
m = n= 1 so there is a horizontal asymptote at y = 1

graph{(x-1)/(x+1) [-10, 10, -5, 5]}

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