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**if**the degree of the function is even

**then**the arrows on the end of the graphs will face the same direction.

**Continuity**

**Continuous Functions have:**

**Discontinuous Functions are:**

**There are 3 types of Discontinuous Functions:**

- Infinite Discontinuity (Asymptotes)
- Jump Discontinuity (Line Disconnects and then Reconnects at a different y value)
- Removable Discontinuity (Open Circle to Represent a whole in the Graph)

**End Behavior**

### **Arrow Direction**

- How a function behaves at either end of the graph
- What happens to the value of f(x) as x increases or decreases without bound

**Limits**

**Where is the graph going as it approaches something?**

- We can't always get an exact answer but we can always tell where it is going?
- For a GREAT INTRO LESSON ON LIMITS check this lesson out: https://geometrycoach.com/lesson-for-the-first-day-of-geometry-class/
- Limits can be mind blowing sometimes. With the activity above students will walk half way to a wall repeatedly until they reach the wall. The problem is they should never reach the wall.
**Welcome to Limits!**

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## Freebie Pre-Requisite Resources for this Lesson:

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- Transforming Parabolas – The Angry Birds Project
- The Nightmare of Exploring Conic Sections
- Area Under a Curve – Is your Umbrella Big Enough?
- The Distributive Property – Cupcakes and Algebra
- How to Teach Patterns and Linear Functions
- Rate of Change and Slope – Ski Through Algebra!
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- Hybrid Flipped Classroom Model
- Ratios and Proportions – Bad Teacher!