### Home > CALC > Chapter 6 > Lesson 6.2.1 > Problem 6-60

6-60.

Find domain, range, holes, and asymptotes for

Horizontal asymptotes, if any, can be found by exploring limit of as

*and limit of*

*as*

*.*

If either, or both, are constants, then the constant(s) is/are the horizontal asymptote(s).

Vertical asymptotes and holes occur where the denominator equals -value of the hole. Find the

*-value too. If the zero in the denominator remains, then that is the vertical asymptote.*

Now that you have found all holes and asymptotes... Use the -values of all holes and vertical asymptotes to restrict the domain. Also consider endpoint(s). Use the

*-values of all holes and horizontal asymptotes to restrict the range. Also, consider endpoint(s).*