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
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 ?
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?