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Function Lingo Activity. Be sure you have a Function Lingo Card and get started. The goal os this activity is to get your mind thinking about functions and why their graphs behavior the way they do. Think about domain, range, shifting, reflections. How to Handle the Summer Packet.

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Function lingo activity
Function Lingo Activity

  • Be sure you have a Function Lingo Card and get started. The goal os this activity is to get your mind thinking about functions and why their graphs behavior the way they do.

  • Think about domain, range, shifting, reflections.


How to handle the summer packet
How to Handle the Summer Packet

  • The summer assignment is in 5 parts.

  • Part 1: I thought I’d grade it the same way I grade homework, and treat it as a big ol’ homework assignment. Be ready to submit on Friday and be ready to ask questions. I may choose to review a few choice problems.

  • Part 2: For Barron’s Chapter 1: I will give a quiz Friday consisting of Barron’s Ch1, all multiple choice.

  • Part 3 and Part 4: I will grade these like homework assignments.

  • Part 5: the Flash Cards. I intend to make a little quiz, maybe some free response, some matching and some multiple choice. Probably about 7 or 8 questions. I haven’t made it yet.


Syllabus books
Syllabus/Books

  • Highlights: Website, homework, practice exams, exam day

  • Check out Books

  • Lesson Activity around “Ch. 1 Limits”



Explore explore explore
Explore, Explore, Explore

With a partner, complete Activity 1 “Approaching Limits” with your TI graphing calculator.


Findings share out
Findings: Share Out

As a class we will share out your discoveries and discuss the answer to likely questions such as

1. What in the world is a limit?2. How can you find a limit?3. Do limits always exist?

4. Do you have a question you want to add?


What is a limit
What is a Limit?

Well, you have explored a bit on your calculators today, but really what is your intention behind finding a limit?

We are most interested in determining "how the function is behaving" as it approaches a value NOT the value of the function. At times, the limit value will also be the function value but keep in mind, we are focused on the behavior!


Function lingo activity

What Do You Think?

not 1

Remember: The limit of a function refers to the value that the function approaches, not the actual value (if any).


Existence of a limit
Existence of a Limit

We just defined what a limit is informally but in order for the limit L to exist (if it didn't exist we would say DNE - does not exist) then the following must be true:

Let f be a function and let c and L be real numbers. The limit of f(x) as x approaches c is L if and only if

IF this does not hold true, the limit of f(x) as x approaches cdoes not exist.

AND THEN


How can we find limits quickly
How Can We Find Limits Quickly?

  • Calculator (analytically)

  • Graphically (looking at a graph)

  • Algebraically


Practice graphical approach
Practice Graphical Approach

It’s your turn to explore your understanding! Remember, state to OWN IT! Ask questions, talk with your table partners, build up a study group!


Assignment
Assignment

Read section 1.2 of the text p. 48-51 only and be sure you can discuss the answers to the following:

1. What are 3 ways to evaluate a limit?

2. Give examples of when a limit fails to exist. Pictures can be helpful.

3. Why are the 3 common types of behavior associated with non-existence of a limit?Complete problems #1-26 all