Question

Identify any discontinuities in the function.

A) There are no discontinuities.

B) There is one discontinuity at x = 3

C) There are two discontinuities at x = 2 and x = 3.

D) There are two discontinuities at x = 0 and x = 3.

Answer 1

There is one discontinuity at x = 3.

Explanation:

The function g(x) has a denominator of (x^2-6x+9), which can be factored into (x-3)^2. Therefore, the function g(x) can be rewritten as:

g(x) = (x^3-9x)/[(x-3)^2]

This function is undefined when the denominator is equal to zero, which occurs when x = 3. Therefore, there is one discontinuity at x = 3, and the correct answer is B) There is one discontinuity at x = 3.