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: Option C
Discontinuity at (−4, −2), zero at (−2, 0)
Step-by-step explanation:
We have the following expression:
[tex]f(x)=\frac{x^2+6x +8}{x+4}[/tex]
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:
[tex](x + 4) (x + 2)[/tex]
So [tex]f(x) =\frac{(x+4)(x+2)}{x+4}[/tex] with [tex]x\neq -4[/tex]
By simplifying the expression we have:
[tex]f(x) =x+2[/tex] with [tex]x\neq -4[/tex]
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
[tex]f(x) =x+2=0[/tex]
[tex]x+2-2=-2[/tex]
[tex]x=-2[/tex]
The zero of the function is: (-2, 0)
The answer is the Option C
