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

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.



  is in the numerator. It is defined for every value of x. There is no problem there.

  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.







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:

Yes the slope to this is -5