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What is the end-behavior function for each of the following functions?

About end behavior:
End behavior describes the shape of the function if we ignore all vertical asymptotes and holes.

If the function has a horizontal asymptote, then that is its end behavior.
If a function has a slant asymptote, then that is it's end behavior.

If a function oscillates as or , then it has no end behavior.

  1. For rational functions, end behavior can often be found using polynomial division (and ignoring the remainder).

  1. Use your calculator to sketch a graph of . What does it look like as and ?

  1. Examine.

    Compare the numerator and denominator. Which has the highest power term as ? (Remember that never gets higher than or lower than .) What does that say about asymptotes?