Question

Anyone good with algebra 2??

Answer 1

A discontinuity is a point that cannot exist because the x-coordinate would cause a problem in the equation. If you have a polynomial in the denominator, you must find which values of x would cause the polynomial in the denominator to evaluate to zero. Since division by zero is undefined, that would cause a discontinuity.

Let's look at your function.

$f(x) = \dfrac{x^2 - 16}{6x - 24}$

$x^2 - 16$  is in the numerator. It is defined for every value of x. There is no problem there.

$6x - 24$  is in the denominator. This is a function defined for every value of x, but since it is in the denominator, we must exclude the x-value that would cause this polynomial to evaluate to zero.

We set it equal to zero and solve the equation for x.

$6x - 24 = 0$

$6x = 24$

$x = 4$

For x = 0, the denominator has a value of zero, so at this point there is a discontinuity in function f(x).

The answer is:

$x \ne 4$