Question

1. Which of these functions has a vertical asymptote at x = -4? There may be morethan one answer, so select all that apply.

Answer 1

A rational function has a vertical asymptote when x becomes a value that makes the denominator equal to 0,

for f(x),

`\begin{gathered} x+4=0 \\ x=-4 \end{gathered}`

for g(x),

`x=0`

for h(x),

`\begin{gathered} 2x^2+11x+12=0 \\ using\text{ the quadratic} \\ x=(-11\pm√(11^2-4*2*12))/(2(2)) \\ x_1=-(3)/(2);x_2=-4 \end{gathered}`

Answer:

The functions f(x) and h(x) have vertical assymptotes at x=-4