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

1 Answer
Nov 29, 2017

Answer:

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.