# Continuity, End Behavior, and Limits – If This Then That

 Would You Rather Listen to the Lesson?
End behaviors can be a fun lesson to teach. There are a lot of “if this then that” situations that arise.

For example, 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:

• no breaks, holes, or gaps
• Can be traced with a pencil without lifting your pencil Limit:
• Approaching a value without necessarily ever reaching it

### Discontinuous Functions are:

• Functions that are not continuous

### There are 3 types of Discontinuous Functions:

1. Infinite Discontinuity (Asymptotes)
2. Jump Discontinuity (Line Disconnects and then Reconnects at a different y value)
3. 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!

## Continuity, End Behavior, and Limits Worksheets – PDFs

1-3 Guided Notes Teacher Edition (Members Only)

1-3 Lesson Plan (Members Only)

1-3 Online Activities (Members Only)

1-3 Video Lesson (Members Only)

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