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?

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?

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.

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

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

Example 1: Is this a function? xf(x)

Example 1: How about this? xf(x)

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)

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

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

How would you describe the numbers that are highlighted below?

What about these?

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.

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

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

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:

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

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

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

Let’s use interval notation to describe some functions.

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!

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.

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