RATL 3 | Lesson 3 | Practice (Asymptotes)

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. 

Go to Making Connections (Asymptotes)