Question

Anyone good with algebra 2??

What are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 6x minus 24?

x ≠ − 4
x ≠ 4
x ≠ − 6
x ≠ 6

Answer 1

Answer: x/=/4

took a teste

Answer 2

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) = (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 \\e 4`