Question

What are the discontinuities of a function?

Answer 1

\[f(x) = \frac{x^2-16}{6x-24}\]

Answer 2

Discontinuities will arise when the denominator goes to zero.
What value of x will cause the denominator to go to zero.

Answer 3

4?

Answer 4

You have changed the denominator. In the original posting it is 6x-24. In your drawing it is 4x - 24. Which is the correct question?

Answer 5

Find when the denominator becomes 0.
4x - 24 = 0
4x = 24
x = 6.

If x = 6, the denominator will become 0.
There is a discontinuity at x = 6.

The domain of this function excludes x = 6.
x should not be 6.

Answer 6

Thanks!