Answer:
c, i believe!!
Step-by-step explanation:
have a good day! <33
Answer:
C. 2, -3
Step-by-step explanation:
Answer:
Step-by-step explanation:
f(x) =
g(x) =
Answer:
See below
Step-by-step explanation:
The given rational function is;
![y=\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%28x-3%29%28x%2B2%29%7D%7B%28x%2B4%29%28x-4%29%28x%2B2%29%7D)
The given function is not continuous where the denominator is equal to zero.
![(x+4)(x-4)(x+2)=0](https://tex.z-dn.net/?f=%28x%2B4%29%28x-4%29%28x%2B2%29%3D0)
The function is discontinuous at ![x=-4,x=4,x=-2](https://tex.z-dn.net/?f=x%3D-4%2Cx%3D4%2Cx%3D-2)
b) The point at x=-2 is a removable discontinuity(hole) because (x+2) is common to both the numerator and the denominator.
The point at x=-4 and x=4 are non-removable discontinuities(vertical asymptotes)
c) The equation of the vertical asymptotes are x=-4 and x=4
To find the equation of the horizontal asymptote, we take limit to infinity.
![\lim_{x\to \infty}\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}=0](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20%5Cinfty%7D%5Cfrac%7B%28x-3%29%28x%2B2%29%7D%7B%28x%2B4%29%28x-4%29%28x%2B2%29%7D%3D0)
The horizontal asymptote is y=0