### 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 or

*, then it has no end behavior.*

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 asand?

Examine.

Compare the numerator and denominator. Which has the highest power term as? (Remember thatnever gets higher thanor lower than .) What does that say about asymptotes?