Create a function with the given features: a vertical asymptote the y-axis, an oblique asymptote y=3x+1, and no x- and y-intercepts. Please...

We know that f(x) and g(x) are asymptotic if f(x)/g(x)  =
1 as x--> infinity. Or f(x) - g(x) = k a constant as x -->
infinity.

We consider the function y(x) =
(3x^2+5x+5)/x

Let f(x) =
3x+5.

Then y(x) - 3x+5 = (3x^2+5x+5)/x - 3x+5  =
{3x^2+5x+5-3x^2-5x) = 5/x  > 0 x for all x ant 5/x = 0 as x -->
infinity.

Therefore  3x+1 is the oblique
asymptote.

Also  for a vertical asymptote, at  x= a , y
should be infinite.

So at x = 0,  y(x) = (3x^2+x+5)/x = 
3x+1 +5/x  is infinte as 5/x = ifinity as x-->
0.

Threfore 3x^2+1  and y axis  are the asmptotes for the
curve y = (3x^2+x+5)/x.