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

Kathryn Sanchez

Kathryn Sanchez

Answered question

2022-09-07

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

Answer & Explanation

illpnthr21vw

illpnthr21vw

Beginner2022-09-08Added 17 answers

Rational equation: f ( x ) = N ( x ) D ( x ) = a n x n + ... b m x 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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