How do you graph and find the discontinuities of #R(x) = (x^2 + x - 12)/(x^2 - 4)#?

1 Answer
bp
Sep 5, 2015

The graph would appear to be as in the given figure.

Explanation:

The graph has two vertical asymptotes at x^2-4=0, that is at x=2 and x= -2

R(x) can also be written as R(x)= 1 +#(x-8)/(x^2-4)#. Thus it has horizontal asymptote at y=1.
At x=0, y=3

The graph would cross x axis at R(x)=0, that is when #x^2+x-12=0# Or, (x+4)(x-3)=0, at x=-4, 3

The graph would appear like this
enter image source here

Related questions
See all questions in Graphs of Rational Functions
Impact of this question
1261 views around the world
You can reuse this answer
Creative Commons License