Find the relative position of the asymptote $y=0$ to the curve of $f\left(x\right)=\frac{2x^3-x^2+1}{x^2+1}$

Determine the relative position of the asymptote $y=3$ to the curve of  $f\left(x\right)=\frac{2x^2-x+3}{x^2+1}$

Determine the relative position of the asymptote $y=-2x+3$ to the curve of  $f\left(x\right)=\frac{4x^2-2x+3}{x}$

Determine the relative position of the asymptote $y=-3x$ to the curve of  $f\left(x\right)=\frac{3x^3+4x-2}{x}$

Find the relative position of the asymptote $y=5$ to the curve of  $f\left(x\right)=\frac{5x^2+2x+1}{x^2+3}$

Find the relative position of the asymptote $y=4$ to the curve of  $f\left(x\right)=\frac{4x^3-2x^2+1}{x^{2+1}}$

Determine the relative position of the asymptote $y=2x$ to the curve of $f\left(x\right)=\frac{3x^2+2x-1}{x}$

Find the relative position of the asymptote $y=-1$ to the curve of  $f\left(x\right)=\frac{x^3-2x+3}{x+1}$

Determine the relative position of the asymptote $y=-x$ to the curve of  $f\left(x\right)=\frac{2x^2+x-3}{x+1}$

Find the relative position of the asymptote $y=2$ to the curve of  $f\left(x\right)=\frac{3x^2+1}{x-1}$