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Home > CALC > Chapter 3 > Lesson 3.4.3 > Problem 3-178
3-178.
Find the end behavior function for 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 asymotote, 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
For rational functions, end behavior can often be found using polynomial division (and ignoring the remainder).
Use your calculator to sketch a graph of
. What does it look like as and ?
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?