the vertical asymptote is x = -4 (option 2)
Explanation:[tex]f(x)\text{ =}\frac{x-3}{x+4}[/tex]
The vertcal asymptote of a function, is the value of x when the denominator is equated to zero:
[tex]\begin{gathered} \text{Denominator = x + 4} \\ \text{equating to zero:} \\ x\text{ + 4 = 0} \\ \text{subtract 4 from both sides:} \\ x\text{ +4 -4 = 0 - 4} \\ x\text{ = -4} \end{gathered}[/tex]
The x - intercept is the value of x when f(x) = 0
[tex]\begin{gathered} f(x)\text{ =}\frac{x-3}{x+4} \\ 0\text{ = =}\frac{x-3}{x+4} \\ 0(x\text{ + 4) = x - 3} \\ 0\text{ = x - 3} \\ x\text{ = 3} \\ x-\text{intercept: }(3,\text{ 0)} \end{gathered}[/tex]
The y-intercept is the value of f(x) when x = 0
[tex]\begin{gathered} f(x)\text{ = }\frac{x-3}{x+4} \\ f(x)\text{ =}\frac{0-3}{0+4} \\ f(x)\text{ = }=\text{ }\frac{-3}{4} \\ y-\text{intercept = (0, -3/4)} \end{gathered}[/tex]
Comparing the results we got and the options, the only option that has same answer as our calculation is the vertical asymptote is x = -4 (option 2)
