Question

What are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 4x minus 24?

Answer 1

dividing x^2 - 16 by 4x - 24 gives the quotient (1/4)x + 3/2

y = (1/4)x + 3/2 would be an asymptote ( discontinuity)

Another would be a vertical discontinuity when x = 6 (this would make the denominator 4x-24 = 0.

Answer 2

x=6 is only the point of discontinuity for the function f(x).

Explanation:

Given a function
`f(x)=(x^2-16)/(4x-24)`.

We have to find the discontinuities of the function.

Point of discontinuities are the points at which the function is not defined.

To find the point of discontinuities we have to put the denominator 0 to find the value of x or to find the point of discontinuity.

∴ 4x-24=0

⇒ 4x=24 ⇒ x=6

Ar x=6 the denominator becomes 0 and the function f(x) is not defined.

Hence, x=6 is only the point of discontinuity for the function f(x).