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. Practice

10. Practice

11. Practice

12. Practice 12

13. Draw a graph such that

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