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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