Rational Functions and Horizontal Asymptotes

Try to answer these questions for our next lesson. Can you suggest an answer to question 3?

Consider the functions given below.
\[f(x)=x^3-2x\qquad g(x)=x^2+4x\qquad h(x)=2x^2+5x-1\]

  1. Form the six possible rational functions using \(f\),\( g\), and \(h\).
  2. Which of the rational functions you have produced have horizontal asymptotes? For any functions that have horizontal asymptotes, write down the equation of that asymptote.
  3. How can you tell when a rational function will have a horizontal asymptote? How can you determine the equation of that asymptote?

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