# Asymptotes

For the following functions find any horizontal and vertical asymptotes. Some functions may have both, others only one.

1. $$f(x)=\dfrac{x-2}{x-3}$$
2. $$f(x)=\dfrac{(x-2)(x-3)}{(x-1)(x-4)}$$
3. $$f(x)=\dfrac{x^2+2}{x(x^2-1)}$$
4. $$f(x)=\dfrac{x^4}{x+1}$$
 Function Horizontal Asymptote Vertical  Asymptote $$f(x)=\dfrac{x-2}{x-3}$$ $$f(x)=\dfrac{(x-2)(x-3)}{(x-1)(x-4)}$$ $$f(x)=\dfrac{x^2+2}{x(x^2-1)}$$ $$f(x)=\dfrac{x^4}{x+1}$$

When you are done, check your answers by graphing them using Desmos Graph the function as well as its asymptotes to get a clear picture of the curves approaching each asymptote.

Check solutions here.