what are the discontinuity and zero of the function f(x) =x^2+6x+8 over x+4
a)discontinuity at (4, 6), zero at (−2, 0)
b)discontinuity at (4, 6), zero at (2, 0)
c)discontinuity at (−4, −2), zero at (−2, 0)
d)discontinuity at (−4, −2), zero at (2, 0)

Option C

Discontinuity at (−4, −2), zero at (−2, 0)

Step-by-step explanation:

We have the following expression:

Note that the function is not defined for x = -4, since the division by zero is not defined

We factor the expression of the numerator.

We look for two numbers that when you multiply them you obtain as a result 8, and by adding both numbers you get as a result 6.

You can check that the numbers that meet these requirements are 4 and 2.

So the factors of the quadratic function are:

So  with

By simplifying the expression we have:

   with

Since the function is not defined for x = -4 then f(x) has a discontinuity at the point (-4, -2)

To find the zero of the function you must equal f (x) to zero and solve for x

The zero of the function is: (-2, 0)

The answer is the Option C

i'm pretty sure the answer would b. 8