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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With a partner, complete Activity 1 “Approaching Limits” with your TI graphing calculator.
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?
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!
What Do You Think?
Remember: The limit of a function refers to the value that the function approaches, not the actual value (if any).
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.
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!
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