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

3-178.

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 *x* →∞ or *x* →−∞, 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 *g*(*x*). What does it look like as *x* →∞ and *x* →−∞?

Examine.

Compare the numerator and denominator. Which has the highest power term as *x* → ∞? (Remember that *y* = sin*x* never gets higher than 1 or lower than −1.) What does that say about asymptotes?