SOLUTION: Graph the rational funxtion f(x)=x^2+5x-6/x^2+2x-3. indentify the vertical and horizontal asymptotes, and any holes in the graph

Algebra ->  Rational-functions -> SOLUTION: Graph the rational funxtion f(x)=x^2+5x-6/x^2+2x-3. indentify the vertical and horizontal asymptotes, and any holes in the graph      Log On


   

Question 295503: Graph the rational funxtion f(x)=x^2+5x-6/x^2+2x-3. indentify the vertical and horizontal asymptotes, and any holes in the graph
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify first.
You can factor numerator and denominator and get rid of common factors, if there are any.
x%5E2%2B5x-6=%28x%2B6%29%28x-1%29
x%5E2%2B2x-3=%28x%2B3%29%28x-1%29

%28x%5E2%2B5x-6%29%2F%28x%5E2%2B2x-3%29=%28x%2B6%29%2F%28x%2B3%29%29
Vertical asymptotes occur when the denominator goes to zero.
For f(x), the denominator goes to zero when,
x=-3
To find horizontal asymptotes, divide numerator and denominator by the highest exponent x term, then take the limit.
f%28x%29=%28x%5E2%2B5x-6%29%2F%28x%5E2%2B2x-3%29

f%28x%29=%281%2B5%2Fx-6%2Fx%5E2%29%2F%281%2B2%2Fx-3%2Fx%5E2%29
in the limit, the crossed out terms go to zero.

So then
lim%28x-%3Einfinity%2C+f%28x%29%29=1
There is a horizontal asymptote at y=1.
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Since there is a division by zero at x=-3, the value of f%28-3%29 is undefined.
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