identify the vertical asymptote(s) of the function. $f(x)=\frac{x + 2}{x^{2}-3x - 4}$\n$x=-4$\n$x=-2$\n$x=-1$…

identify the vertical asymptote(s) of the function. $f(x)=\frac{x + 2}{x^{2}-3x - 4}$\n$x=-4$\n$x=-2$\n$x=-1$\n$x=1$\n$x=2$\n$x=4$\ndone

identify the vertical asymptote(s) of the function. $f(x)=\frac{x + 2}{x^{2}-3x - 4}$\n$x=-4$\n$x=-2$\n$x=-1$\n$x=1$\n$x=2$\n$x=4$\ndone

Answer

Explanation:

Step1: Factor the denominator

Factor $x^{2}-3x - 4=(x - 4)(x+1)$. So $f(x)=\frac{x + 2}{(x - 4)(x + 1)}$.

Step2: Find values for vertical asymptotes

Vertical asymptotes occur where the denominator is zero and the numerator is non - zero. Set the denominator equal to zero: $(x - 4)(x + 1)=0$. Solving gives $x=4$ and $x=-1$. When $x = 4$, the numerator $x + 2=4+2=6\neq0$. When $x=-1$, the numerator $x + 2=-1 + 2=1\neq0$.

Answer:

C. $x=-1$, F. $x = 4$