Question

PLEASE HELP ME!!!!

Answer 1

This is what I got, but you might want to double check me because I'm not that good at math (this is what I got for the discontinuity);

1. f(x)= x^2+6+8/x+4

*x+4=0                                      

-4 -4                                      

 x= -4

This means that x cannot equal -4

2. f(x)= (x+2)(x-4)/(x+2)(x+2)

*Note: When I did my calculations, I cancelled out all (x+2) binomials except for one in the denominator*

f(x)= x-4/x+2

*x+2=0                                      

   -2 -2                                      

     x= -2

This means x cannot equal -2

*You may want to check my work, but I believe that your answer is going to be either C or D. Personally, I assume it's C, but that's just me. Anyway, it's probably going to be C or D, or at least that's what I think.*

Answer 2

Answer: Option C

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

Step-by-step explanation:

We have the following expression:

$f(x)=\frac{x^2+6x +8}{x+4}$

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:

$(x + 4) (x + 2)$

So $f(x) =\frac{(x+4)(x+2)}{x+4}$  with $x\neq -4$

By simplifying the expression we have:

$f(x) =x+2$    with $x\neq -4$

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

$f(x) =x+2=0$

$x+2-2=-2$

$x=-2$

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

The answer is the Option C