RATL 3 | Lesson 3 | Practice (Asymptotes)

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

1) \(f(x)=\Large \frac{x-2}{x-3}\)

2) \(f(x)=\Large \frac{(x-2)(x-3)}{(x-1)(x-4)}\)

3) \(f(x)=\Large \frac{x^2+2}{x(x^2-1)}\)

4) \(f(x)=\Large \frac{x^4}{x+1}\)

Function Horizontal Asymptote Vertical  Asymptote
\(f(x)=\Large \frac{x-2}{x-3}\)
\(f(x)=\Large \frac{(x-2)(x-3)}{(x-1)(x-4)}\)
\(f(x)=\Large \frac{x^2+2}{x(x^2-1)}\)
\(f(x)=\Large \frac{x^4}{x+1}\)

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)