1. End Behavior Unit 3 Lesson 2c

2. End Behavior End Behavior is how a function behaves as x approaches infinity ∞ (on the right) or negative infinity -∞ (on the left). We write “the limit as x goes to infinity” as

3. Example 1: Describe the End Behavior Describe the end behavior of

4. Example 2 : Describe the End Behavior Describe the end behavior of 1. If the limit approaches a constant as x goes to + or – infinity, we say it has a horizontal asymptote at y = that constant. 2.Does the function above have a horizontal asymptote?

5. Examine the end behavior and asymptotes of Example 3: Describe the End Behavior Any horizontal asymptotes?

6. Examine the end behavior of Conclusion: Example 4: Describe the End Behavior

7. Determine the end behavior of the odd function Example 5: Describe the End Behavior

8. Determine the end behavior of the function Example 6: Describe the End Behavior

9. Determine the end behavior of the function Example 7: Describe the End Behavior

10. Closure: Possible End Behaviors: There are three possible end behaviors: 1. The values of f(x) can increase or decrease without bound (to  or -  ) 2. The values of f(x) can approach some number L 3. The values of f(x) can follow neither of these patterns (such as oscillating between two values). Which functions on the previous slides match to the types described above?