SOLUTION: List the vertical and horizontal asymptotes of each function, and sketch its graph. g(x)= x^2/x^2-1

Algebra ->  Rational-functions -> SOLUTION: List the vertical and horizontal asymptotes of each function, and sketch its graph. g(x)= x^2/x^2-1      Log On


   

Question 890254: List the vertical and horizontal asymptotes of each function, and sketch its graph.
g(x)= x^2/x^2-1
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You really mean this: g(x)= (x^2)/(x^2-1)

The rendering tags will make it show, g%28x%29=x%5E2%2F%28x%5E2-1%29.

You can find zeros of the denominator using simple factorization:
g%28x%29=%28x%5E2%29%2F%28%28x-1%29%28x%2B1%29%29
The numerator and denominator share no factors. The denominator is undefined for x=1 and x=-1. This makes vertical asymptotes at x=-1 and x=1.

You can check around the critical points to test for signs and find a shape for the graph.

graph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx%5E2%2F%28x%5E2-1%29%29

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor did not mention the fact that since the degree of
the numerator is equal to the degree of the denominator, (both
have degree 2) the horizontal asymptote is 

y+=%28LEADING_COEFFICIENT_OF_NUMERATOR%29%2F%28LEADING_COEFFICIENT_OF_DENOMINATOR%29

%22g%28x%29%22=+red%281%29x%5E2%2F%28red%281%29x%5E2-1%29

y=red%281%29%2Fred%281%29 or

y=1 a horizontal line through 1 on the y-axis.



The green lines are the asymptotes, vertical x=1, x=-1, and 
horizontal y=1.

Edwin