Question

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

Answer 1

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

Answer 2

Choices:

Answer 3

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

Answer 4

That leaves x-9 in the denominator.

Answer 5

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.

Answer 6

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

Answer 7

Correct?

Answer 8

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.