Question

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)`?

Answer 1

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`