Question

determine the equations of the asymptotes :
g(x)=2x^2+1/x+3

Answer 1

is this the problem: \(\large g(x)=\frac{2x^2+1}{x+3} \) ???

Answer 2

yes

Answer 3

to find the vertical asymptote, just set the denominator = 0 and solve for x...
to find the slant asymptote, do long division and forget about the remainder.

Answer 4

this expression has only 1 vertical and 1 slant (oblique) asymptote.