2. Warm Up  Sit in your usual seat. Put your tracking sheet and homework on the corner of your desk. Answer the following questions on a separate sheet of paper (and keep this paper out throughout class):  1. How did you feel about the test in general yesterday? What specifically was easy? What specifically was hard?  2. Write down every single thing you can think of when you hear the word function. What does a function have? What makes something a function or not?

3. Unit 2—What are we learning?  Properties of functions:  for the rest of 1 st quarter, it is going to be very important for us to know how to talk about functions, some common characteristics of functions, and how to tell whether or not something is a function.  So…what does that mean for today?

4. Today’s Objectives  SWBAT describe a function and its domain and range.  SWBAT use interval notation to describe intervals of points.  SWBAT use interval notation to describe increasing and decreasing intervals of points.

5. What is a function?  It is a rule that spits out a y-value for every x that you put in it.

6. What is a function?  In other words…  For every x value, there is only ONE y value.  What does this not say?

7. Example 1: Is this a function? xf(x) -23 4 5 06 17

8. Example 1: How about this? xf(x) -23 4 05 16 27

9. Formal Definition of a Function A function from a set D to a set R is a rule that assigns to every element in D a unique element in R. The set D of all input values is the domain of the function and the set R of all output values is the range of the function. y = f(x)

10. Domain  Domain: the set of _____ values for a given function. Also known as:

11. Range  Range: the set of _____ values for a given function. Also known as:

13. How would you describe the numbers that are highlighted below?

14. What about these?

15. Bounded Intervals  Bounded intervals: intervals that contain a highest and a lowest point  Example: x > -2, x < 3  Interval Notation:  * Always put smaller number first.

16. Unbounded Intervals  Unbounded intervals: intervals that approach positive or negative infinity  Example: x > -4  Interval Notation:

17. Included Points  Included points: points that are on the end of an interval and are included in the set  Example: x ≤ -1  Interval Notation:

18. Excluded Points  Excluded points: points that are on the end of an interval and are not included in the set  Example: x < 2  Interval Notation:

19. Union  Union: a union is used to combine two separate sets  Example: x 1  Interval Notation:

20. Examples 2 and 3: Describe the following in interval notation and draw. (Do this on the same sheet as your warmup.) x < 3x < -4, x ≥ 2

21. Example 1: Describe the following in inequality form and draw. (Do this on the same sheet as your warmup.) [-4, 3)(-∞, 2] U (4, ∞)

22. Let’s use interval notation to describe some functions.

29. For the last part of class  Complete the practice problems.  To get your classwork stamp, you must complete at LEAST questions 1 –  Your homework is to finish the rest of the practice problems!

30. Exit Ticket  I’m going to start having you complete an exit ticket at the end of class most days.  This provides me with valuable information, such as:  Did you understand what we did that day?  Did I do a good job teaching?  Did you do a good job learning?  While you are SILENTLY AND INDEPENDENTLY completing your exit ticket, I will walk around and give you your class work stamp for the day if you completed what you needed to.

31. Exit Ticket 1. Describe the following inequality in interval notation. x ≥ 2, x<7 2. Fill in the blanks. A _________ is a rule that assigns numbers from the ________ to the __________. A* Vertical line test, domain, range B* Function, range, domain C* Vertical line test, domain, range D* Function, domain, range