How do you graph #y=(x^2-4)/(x+1)# using asymptotes, intercepts, end behavior?

1 Answer
Oct 9, 2016

graph{(x^2-4)/(x+1) [-10, 10, -5, 5]}


The asymptote of the graph is x=-1. To find the asymptote set the denominator equal to 0 and solve for x. Thus, -1 is the only value for x such that when it is plugged in, there is no value for y (any number divided by zero is undefined).

To solve for the x-intercepts set the numerator equal to zero and solve for x. I would suggest factoring or adding 4 and taking the square root of 4. Either way, you will find out the x-intercepts of the graph are positive and negative two.
To solve for the y-intercepts set x equal to zero and solve for y. Y=-4, and thus the graph passes through the y-intercept at the point (0,-4).

First, plug in the intercepts and asymptote. Then, by plugging in x-values and solving for y-values, you can plot other points and determine the graph.