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.

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Check solutions here. 

Go to Making Connections (Asymptotes)