How do you graph y=(x+2)/(x-3) using asymptotes, intercepts, end behavior?

1 Answer
Nov 29, 2017

here is the graph:
enter image source here

Explanation:

To graph y=(x+2)/(x-3):

NPV= 3
There are no common factors between the numerator and denominator so the vertical asymptote is 3.
VA=3

Horizontal Asymptote:
deg N = degD

when the numerator and denominator equal the same, you divide the leading coefficients to get the horizontal asymptote.

HA: y= x/x= 1

There is no slant asymptote.

Find behaviour near V.A (generally =+/-0.1 away):

at x=3.1 = +/+ = positive infinity

at x=2.9 = +/- = negative infinity

so x=3.1 will start to the right of the vertical asymptote in quadrant I, and x=2.9 will start to the left of the vertical asymptote in quadrant IV.

The x intercept is the zero of the numerator, so x=-2
To find the y intercept, set x=0 into the equation.

y=(0+2)/(0-3)
y=2/-3 or -0.6667

Join the points smoothly.