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# Find the​ domain, points of​ discontinuity, and​ x- and​ y- intercepts of the rational function. Determine whether the discontinuities are

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Find the​ domain, points of​ discontinuity, and​ x- and​ y- intercepts of the rational function. Determine whether the discontinuities are removable or​ non-removable.       y=18−6xx2−9x+18

What is the domain of the​ function?

A. The set of all real numbers except y=3 and y=6

B. The set of all real numbers except x=0, x=3, and x=6

C. The set of all real numbers except y=0, y=3, and y=6

D. The set of all real numbers except x=3, and x=6

Dec 15, 2020

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I think  this is

(18 - 6x)                   6 ( 3 - x)                     -6

___________   =   ____________   =    _________

x^2 - 9x+ 18            (x - 3) ( x - 6)            x - 6

We will have  a vertical asymptote  when    x -  6  = 0   ⇒     x   =    6

Additionally.....we  will  have a "hole"   when  x = 3

So the domain is   all reals except  x =  3  and x  = 6

Dec 16, 2020
edited by CPhill  Dec 16, 2020