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

6-60.

Horizontal asymptotes, if any, can be found by exploring limit of *f*(*x*) as *x*→∞ and limit of *f*(*x*) as *x*→−∞.

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 0. If the zero on the denominator 'cancels out', then that is the *x*-value of the hole. Find the *y*-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 *x*-values of all holes and vertical asymptotes to restrict the domain. Also consider endpoint(s). Use the *y*-values of all holes and horizontal asymptotes to restrict the range. Also, consider endpoint(s).