1. 23 – Limits and Continuity I – Day 1 No Calculator
Piecewise Investigations
23 – Limits and Continuity I – Day 1 No Calculator

2. Limit – the intended height of a function
Previously Studied Limits
End behavior of polynomial functions
End behavior of exponential functions

3. “limit as x approaches a from the left = limit as x approaches a from the right”
“left hand limit = right hand limit ”

5. Remember: A limit is the intended height of a function.

6. Remember: A limit is the intended height of a function.

8. Given the graph of h(x) below, evaluate each limit.6 2

9. Given the graph of k(x) below, evaluate each limit.4 –4 –8 –4

10. Notice……
Evaluating these limits used the left piece...
values less than a.

11. Notice……
Evaluating these limits used the right piece...values greater than a.

12. Since –10 is in the
first piece….
Since 0 is in the
second piece….
Since 9 is in the
fourth piece….
Since 5 is in the
third piece….
Since 12 is in the
fourth piece….
Notice……
by substitution into the piece.

13. Notice……
by left-hand and right-hand limits.

14. Evaluate the following limits.