How do you find the domain, points of discontinuity and the x and y intercepts of the rational function #y=(12-6x)/(x^2-8x+12)#?

1 Answer
May 19, 2017

Answer:

Domain : #x in RR , x != 6# or # (-oo,6) uu(6,oo) #
Points of discontinuity are #x=6 , x=2#, x intercept as # x=2#, y intercept as #y=1#

Explanation:

#y = (12-6x)/(x^2-8x+12) or y = (-6 cancel((x-2)))/((x-6) cancel((x-2)))# or

#y= -6/(x-6) # domain : x !=6 ,#x in RR , x != 6# or # (-oo,6) uu(6,oo) #

Points of discontinuity are #x=6 , x=2#, but #x=2# is removable discontinuity.
Putting #x=0# we get y intercept as #y=12/12=1#

Putting #y=0# we get x intercept as # 12-6x=0 or x=2#