Given:
[tex]f(x)\text{ = }\frac{x^2+9x+8}{3x^2-24x-27}[/tex]First, we determine the excluded values:
3x² - 24x - 27 = 0
3(x² - 8x - 9) = 0
3(x - 9)(x + 1) = 0
x ≠ -1 and x ≠ 9
Now we evaluate limits on -1 and 9:
[tex]\lim _{x\to-1}\frac{x^2+9x+8}{3x^2-24x-27}\text{ = }\frac{-7}{30}[/tex][tex]\lim _{x\to9}\frac{x^2+9x+8}{3x^2-24x-27}\text{ =Doesn't exists.}[/tex]So, x = 9 corresponds to a ertical asymptote
