## Section 2.3 - Continuity

**Essential Question(s):**

What does it mean for a function to be continuous?

**Follow**__these three steps__to complete this "flip" lesson.**STEP 1: Preparation**

__Title__your spiral with the heading above and

__copy__the essential question(s).

**STEP 2: Vocabulary & Examples**

__Copy__and

__define__the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed.

__Review__the following examples and

__copy__what is necessary for you. Use the guiding questions for your cornell notes.

__Continuity at a Point__

- What is a continuous function? (pg 78)
- How are limits used with continuity? (Ex 1 pg 78-79)
- What is continuity at a point? (pg 79)
- What is discontinuity? (pg 79)
- How do you find points of continuity and discontinuity of the greatest integer function? (Ex 2 pg 79)
- Review the types of discontinuities. (pg 80)

__Continuous Functions__

- What is a continuous function? (pg 81)
- What about the basic functions and continuity? (pg 81 & Ex 3)

__Algebraic Combinations__

- What about combinations of continuous functions? (pg 81)
- What are the properties of continuous functions? (pg 82)

__Composites__

- What about composite functions and continuity? (pg 82 Theorem 7)
- How do you show a composite function is continuous? (Ex 4 pg 82)

__Intermediate Value Theorem for Continuous Functions__

- What is the intermediate value theorem? (pg 83)
- What is a graphing consequence of the intermediate value theorem? (pg 83)
- How can you apply the intermediate value theorem? (Ex 5 pg 83-84)

**STEP 3: Reading**

__Read__the following page(s) and take any extra notes as needed.

- Read pages 78 - 84.
- Make sure to read the paragraphs between the examples and sidebar snippets.