Question Type 1: Finding the asymptotes and intercepts of rational functions of the form f(x)=(ax+b)/(cx^2+dx+e) Exercises

Find the vertical asymptote(s), horizontal asymptote, x-intercept and y-intercept of $f(x)=\frac{4x+1}{x^2+2x+5}$

Find the vertical and horizontal asymptotes, x-intercept and y-intercept for $f(x)=\frac{3x+4}{5x^2+3x-2}$.

Find the vertical asymptotes, horizontal asymptote, x-intercept and y-intercept of $f(x)=\frac{-x+2}{x^2-5x+6}$.

Find the vertical asymptotes, horizontal asymptote, x-intercept and y-intercept of $f(x)=\frac{7x-5}{x^2-1}$.

Find all asymptotes and intercepts of the function $f(x)=\frac{5x-2}{x^2-4x+3}$

Determine the vertical and horizontal asymptotes, x- and y-intercepts of $f(x) = \frac{-3x+6}{2x^2-8}$.

Determine the vertical asymptotes, horizontal asymptote, x-intercept and y-intercept of $f(x)=\frac{x-4}{x^2-9}$

Determine all asymptotes and intercepts of $f(x)=\frac{x+2}{3x^2-12x+12}$

Determine all asymptotes and intercepts of the function $f(x)=\frac{x-1}{x^2+4x+4}$

Find the vertical asymptotes, horizontal asymptote, $x$-intercept and $y$-intercept of the function $f(x)=\frac{2x+3}{x^2+x-1}$.

Determine the asymptotes and intercepts of $f(x)=\frac{2x-7}{x^2-2x-3}$

Determine the asymptotes and intercepts of $f(x)=\frac{-2x-3}{x^2-2x}$