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

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.