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Factoring Hole Horizontal Asymptote How-To Precalculus Rational Function Vertical Asymptote

Matching a Rational Function with its Graph

Author: Elena Welch

The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Reveal Answer" to reveal the answer to the problem.

Problem: Match the given function with its graph below\[
        f(x)=\frac{3x^3}{x^2+2x}
    \]with its graph below.


  1. A graph with a vertical asymptote at x equals negative two, approaches y equals zero on both ends, and a hole when x equals 0

  2. A graph with a vertical asymptote of x equals negative 2, a slant asymptote, and a hole when x equals 0

  3. A graph with a vertical asymptote at x equals zero and approaches y equals one on both ends

  4. A graph with vertical asymptotes at x equals negative two and three and y approaches zero on both ends

The correct graph is b. 

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