The limit as x approaches a number whose function value is definite:

3. A limit gives us language for describing how function values (y-values) behave as the domain values (x-values) approach some particular number (or ∞ or -∞). • In other words, a limit tells us: • what the y-values of a function are approaching as x approaches some value c (but not necessarily equal to c) or it tells us • the intended y-value of a function as x approaches c (we will see this when x approaches a hole).

4. The limit as x approaches a number whose function value is definite:

5. The limit as x approaches an asymptote:(limits that fail to exist)

6. : Parent signature and test corrections on loose-leaf!!! Another example of when a limit fails to exist:

7. The limit as x approaches a hole:

8. Some more examples:

10. SUMMARY OF THE RELATIONSHIP BETWEEN HORIZONTAL AND VERTICAL ASYMPTOTES AND LIMITS: HORIZONTAL ASYMPTOTE VERTICAL ASYMPTOTE

11. END-BEHAVIOR MODEL (EBM) FOR RATIONAL FUNCTIONS: HOW DO WE USE THIS END-BEHAVIOR MODEL (EBM): EXAMPLE OF (EBM):

12. WHEN HAVE WE USED THE “EBM” IN A SIMILAR FASHION? To find horizontal asymptotes. LET’S EXAMINE THE PREVIOUS EXAMPLE MORE CLOSELY:

15. Review for Test: