Practice Problems

Graph the following rational functions. Identify any holes or asymptotes.

\(\textbf{1)}\) \(f(x)= \displaystyle\frac{4x+5}{x+1}\)

 

\(\textbf{2)}\) \(f(x)= \displaystyle\frac{5}{x^2-4}\)

 

\(\textbf{3)}\) \(f(x)= \displaystyle\frac{x^2-9}{x^2-3x}\)

 

\(\textbf{4)}\) \(f(x)= \displaystyle\frac{2x+5}{4x-3}\)

 

\(\textbf{5)}\) \(f(x)= \displaystyle\frac{4x}{x^2+4x+4}\)

 

\(\textbf{6)}\) \(f(x)= \displaystyle\frac{x^2+6x+9}{x^2-9}\)

 

\(\textbf{7)}\) \(f(x)= \displaystyle\frac{x^2+3x+2}{5x+5}\)

 

\(\textbf{8)}\) \(f(x)= \displaystyle\frac{x^3-1}{x^2-1}\)

 

Challenge Problems

\(\textbf{9)}\) \(f(x)= \displaystyle\frac{x^2-1}{x^4-1}\)

 

\(\textbf{10)}\) \(f(x)= \displaystyle\frac{x^3-8}{x^2+2x+4}\)

 

See Related Pages\(\)

\(\bullet\text{ Vertical Asymptotes}\)
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\(\bullet\text{ Horizontal Asymptotes}\)
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\(\bullet\text{ Slant Asymptotes}\)
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