### Home > APCALC > Chapter 3 > Lesson 3.4.3 > Problem 3-178

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.*

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?