Question

How to find asymptotes of piecewise functions?

A) Evaluate the limit at critical points
B) Find the domain of each piece
C) Use the horizontal asymptote rule
D) Apply the vertical asymptote rule

Answer 1

To find asymptotes of piecewise functions, you can follow steps to evaluate limits at critical points, find domains, use horizontal asymptote rule, and apply vertical asymptote rule.

Step-by-step explanation:

To find asymptotes of piecewise functions, you can follow these steps:

1. Evaluate the limit at critical points where the function may have a vertical asymptote.
2. Find the domain of each piece of the function. This will help identify any discontinuities and vertical asymptotes.
3. Use the horizontal asymptote rule to determine the behavior of the function as x approaches positive or negative infinity.
4. Apply the vertical asymptote rule to find any vertical asymptotes. This involves checking the limits as x approaches the values where the function may have vertical asymptotes.

By following these steps, you can determine the asymptotes of piecewise functions.