What are the points of discontinuity? Are they all removable? y=(x-3)/x^2-12x+27

Question

anonymous · Answer

$$y=\frac{ (x-3) }{ x ^{2} -12x+27 }$$

anonymous · Answer

Choices:

anonymous · Answer

Factor the denominator and look at what cancels (if anything).

anonymous · Answer

That leaves x-9 in the denominator.

anonymous · Answer

That which makes the cancelled binomial = 0 represents a "hole" or point of discontinuity.  Normally the zeroes of the denominator are vertical asymptotes, but when a factor of the denominator cancels you get holes instead.

anonymous · Answer

The answer must be x=9, x=3; no

anonymous · Answer

Correct?

anonymous · Answer

The graph is discontinuous at 9 and 3, but only 3 is removable.  At x=3 there is a hole but the function would be continuous to that point and just after.  At x=9 the graph is totally disconnected separated by an asymptote.