Find the vertical asymptote of \(f(x)=\frac{1}{x-5}\).

Find the horizontal asymptote of \(f(x)=\frac{3x+1}{x-2}\).

Find the horizontal asymptote of \(f(x)=\frac{2x^2-1}{5x^2+x}\).

Find the vertical asymptotes of \(f(x)=\frac{x+1}{x^2-9}\).

For \(f(x)=\frac{x^2+1}{x^3+1}\), find the horizontal asymptote.

For \(f(x)=\frac{x^2-4}{x-2}\), explain whether \(x=2\) is a vertical asymptote.

Find the slant asymptote of \(f(x)=\frac{x^2+3x+1}{x+1}\).

Find all vertical and horizontal asymptotes of \(f(x)=\frac{2x^2}{x^2-1}\).

Compare the end behaviour of \(f(x)=\frac{4x^3-x}{2x^3+5}\) as \(x\to\infty\) and as \(x\to-\infty\).

For \(f(x)=\frac{x^2-1}{x^2-3x+2}\), identify any holes and vertical asymptotes.