1. Warmup: Let’s Practice Graphing Piecewise Functions Ourselves

2. Example Problem #2

3. Finding Limits Graphically
PRE-CALCULUS UNIT 1 Day 2
Finding Limits Graphically

4. What is a limit?
A limit describes how the output values of a function behave as input values approaches some given #, “c”
Notation:
Read “limit of f(x) as x approaches c is equal to L”

5. Kinds of limits THE Limit (double-sided limit) Left-hand limit
Limit of f(x) as x approaches c from either direction.
Only exists if left-hand and right-hand limits are the same.
Left-hand limit
Limit of f(x) as x approaches c from the left side.
Right-hand limit
Limit of f(x) as x approaches c from the right side.

7. Misconception #1 A function does not have to be defined at “c” in order for the limit to exist.

8. Misconception #2 If a function is defined at “c”, f(c) does not necessarily have to equal L.

9. Two Cases for When the Limit is D.N.E. (Does Not Exist)
Behavior differs from the left
and right
Oscillating Behavior
Ex/

10. Practice

11. Practice

12. Practice

13. Practice 13

14. Draw a graph such that

15. Draw a graph such that

16. Draw a graph such that

17. Draw a graph such that

18. Draw a graph such that

19. Draw a graph such that