Question

What are the points of discontinuity?

Answer 1

x = 9, x = 3

Explanation:

Given

y =
`(x-3)/(x^2-12x+27)`

The denominator of the rational function cannot be zero as this would make y undefined.

Equating the denominator to zero and solving gives the values that x cannot be, that is

x² - 12x + 27 = 0

(x - 9)(x - 3) = 0

Equate each factor to zero and solve for x

x - 9 = 0 ⇒ x = 9

x - 3 = 0 ⇒ x = 3

Thus x = 9, x = 3 are excluded values and the points of discontinuity