What are the discontinuity and zero of the function f(x) = quantity x squared plus 6 x plus 8 end quantity over quantity x plus 4Discontinuity at (4, 6), zero at (−2, 0)Discontinuity at (4, 6), zero at (2, 0)Discontinuity at (−4, −2), zero at (−2, 0)Discontinuity at (−4, −2), zero at (2, 0)

Answer:Discontinuity at (-4,-2), zero at (-2,0).Step-by-step explanation:We are given that a function [tex]f(x)=\frac{x^2+6x+8}{x+4}[/tex]We have to find the discontinuity and zero of the given function.Discontinuity: It is that point where the function is not defined.It makes the function infinite.[tex]f(x)=\frac{x^2+4x+2x+8}{x+4}[/tex][tex]f(x)=\frac{(x+4)(x+2)}{x+4}[/tex]When x=-4 then [tex]f(-4)=\frac{0}{0}[/tex] It is indeterminate form Function is not defined After cancel out x+4 in numerator and denominator  then we get [tex]f(x)=x+2[/tex]Substitute x=-4[tex]f(-4)=-4+2=-2[/tex]Therefore, the point of discontinuity is (-4,-2).Zero: The zero of the function is that number when substitute it in the given function then the function becomes zero.When substitute x=-2Then , [tex]f(0)=-2+2=0[/tex]The function is zero at (-2,0).Hence, option C is true.