WELCOME TO ALGEBRA!! Find your name and sit in that seat. Materials you will need today and everyday: Pencil Eraser Notebook Paper Calculator (graphing calculator-TI 83/84) *If you do not have one today, DON’T WORRY! Binder to put all of your stuff in! (Keep it organized) Label your paper with the objective and be ready to start class.

I have high expectations for ALL students. I expect everyone to work to the best of their ability. If you have any questions on the material, PLEASE ASK! I am always available to help. Also, use other resources for help! (After school tutoring, study with peers, ask another teacher, etc…) Expectations:

To be responsible for his/her own behavior—you choose how you react to different events To understand that inappropriate/disruptive classroom behavior interferes with the teaching and learning of others To respect the feelings and right of others To refrain from the use of physical force or the threat of physical force To attend school and class every day and be on time prepared to work To do what any teacher or adult in the building reasonably requests of you To be aware of and follow all school and county rules and procedures (cheating, electronics, tardiness, dress code, IDs, etc…) Ashley’s Student Responsibilities:

I have no tolerance for ANY cheating. This means no cheating on ANY assignment (tests, warm-ups, classwork, and homework). Cheating results in NO CREDIT and possibly further disciplinary action. Cheating:

1 st - Warning 2 nd - Phone Call 3 rd - Lunch Detention (served the 1 st half of student’s assigned lunch—if not served, a referral will be sent) 4 th - Referral 5 th or more- Referral Tardy Policy:

Notebook: Each student is expected to keep materials for this class organized. Students will be required to turn in homework and classwork (includes warm-ups) for a grade. Students who are absent are expected to get warm-ups, notes, classwork, and homework from a student in the class. Homework Classwork Participation (10%):

One per chapter Quizzes are given to help you gage where you stand on the material before a test. Quizzes must be made up with in 2 school days from the return to school to count for full credit Quizzes (25%):

One per chapter You are responsible for preparing in advance for scheduled tests. If you are absent the day before a scheduled test, you are still required to take the test as scheduled. If you are absent the day of a scheduled test, you have one weeks to complete the make-up test. Tests (40%):

Will be counted as TWO test grades Mid-Term Exam

Will be weighted as 25% of your final grade. Final Exam

A 93% - 100% B 85% - 92% C 77% - 84% D 70% - 76% F below 70% Grading Scale:

There are a limited number of graphing calculators available in class. If possible please provide your own calculator for in class and at home use. If a student has to use one of the teacher’s calculators during class, the student is responsible for checking the calculator in and out. If the student does not return the calculator at the end of the class period, the student will be held accountable for replacing the calculator and a fee will be charged to the student’s account. Calculator Policy:

If you would like to check out a book you may. Each student is responsible for their assigned book. If the book is not returned by the end of the semester, the student is responsible for replacing the textbook and a fee will be charged to the student’s account. Textbook Policy:

Students will be given assigned seats. Seating assignments will change periodically throughout the semester. Please let me know if you have any seating requests. Seating Assignments:

Students will be assigned 3 “out the door” passes each nine weeks. This includes restroom, locker, another teacher’s class, library etc… Once a student has exceeded their limit of passes, the student must serve after school detention in exchange for an “out the door” pass. These passes do not roll over. No student may leave class without a pass and his/her ID/student handbook. Restroom/Hall Pass Policy:

I will be available after school ever Monday and Tuesday from 3:30-4:30!! I will be available every morning upon your arrival. After School Tutoring!!!

 Progress reports will be sent out on February 20 th and May 8 th. ◦ It is expected that progress reports be brought home, signed by the parent/guardian, and returned to school the next day. A student or parent/guardian always has the right to request a progress report at any time. ◦ PAM  Report cards will be sent out on April 5 th and June 12 th. Progress Reports/Report Cards:

Please read over the syllabus with your parent/guardian! Bring back the signed student data sheet tomorrow! Keep the syllabus in your binder for reference! HOMEWORK– student info, please complete and turn in tomorrow with signed student data sheet. Bring back Signed!!!

I am looking forward to working with you this semester! Please know that I am always available to help you in any way that I can, but ultimately your effort and work will determine your success in this class.

Introduction to Functions 1/23/13 A single output for every input.

Is your keyboard functional? Suppose you type the letter “J” on your keyboard… And sometimes you get this Is this keyboard functional? J K And sometimes you get this Doesn’t seem functional to me…

NO! Of course not. When you type the letter “J” on your keyboard… Should output “J” 100% of the time! You want the letter “J” gosh darnit! J Now this is a “Functional” Keyboard!

Is this keyboard functional? Well, suppose you typed the letter “3” on your keypad… And this input gave you: Is this keyboard functional? 3 There’s no problem with that, right?! Or decided to type it on the top of your keyboard… And this input also gave you:

Relation (1)32 mpg (2)8 mpg (3)16 mpg (A) (C) (B)

Right. So, as long as there isn’t more than 1 output for each input, we have a FUNCTION! It’s ok if two different inputs give us the same output. BUT 1 INPUT GIVING US 2 OR MORE OUTPUTS?? NO WAY IS THAT FUNCTIONAL!

Definition of a Relation A Relation maps a value from the domain to the range. A Relation is a set of ordered pairs. The most common types of relations in algebra is ordered pairs

The relation {(2,1), (-1,3), (0,4)} can be shown by 1) a table. 2) a mapping. 3) a graph. xy

Mapping x-1047 y36-13 You do not need to write 3 twice in the range!

Is your microwave functional? Suppose you put your favorite pizza in your microwave… And sometimes you got this Is this microwave functional? And sometimes you got this Would you consider your microwave functional?

Is this blender functional? Well, suppose you put some apples in your blender… And you got applesauce this way: Is this blender functional? There’s probably nothing wrong with your blender. It’s functional! Then you decided to put some applesauce in… And applesauce this way!

Domain and Range The values that make up the set of independent values are the domain The values that make up the set of dependent values are the range. State the domain and range from the 4 examples of relations given.

In Mathematics, functions have an independent variable (an input) usually called “x” The dependent variable (the output) is called f(x) which is read “F of X” We can, and often do, let y= f(x) and we say “y is a function of x” DO NOT BE CONFUSED! f(x) DOES NOT MEAN f times x, or fx, f*x

Mike’s cell phone is part of a family plan. If he uses more minutes than his share, then there are fewer minutes available for the rest of the family. *identify independent and dependent variables*

Warm up! Give a real life example of something that IS functional and explain how. Give a real life example of something that IS NOT functional and explain why. How are mathematical functions related to real life functions?

Vertical Line Test for Functions If a vertical line intersects a graph once and only once for each element of the domain, then the graph is a function.

x y x y Does the graph represent a function? Name the domain and range. No D: x ≥ 1/2 R: all reals No D: all reals R: all reals

x y x y Does the graph represent a function? Name the domain and range. Yes D: all reals R: all reals Yes D: all reals R: y ≥ -6

x + y = 4 What about decimals? If x = 2.6 then y = ? y = 1.4 Now, let’s graph the pairs of numbers we have listed.

(1, 3) (2, 2) (4, 0) (-1, 5) (2.6, 1.4) Connect the points on your graph. What does the graph look like?

It is a straight line! It is a linear function. All solutions for the equation x+y=4! Is (3, -1) a solution to this equation? NO! You can check by graphing it or plugging into the equation! What does the line represent?

Given the following table, show the relation, domain, range, and mapping. x-1047 y36-13 Relation = {(-1,3), (0,6), (4,-1), (7,3)} Domain = {-1, 0, 4, 7} Range = {3, 6, -1, 3}

INPUT, “x” FUNCTION, “f ” OUTPUT, “f(x)”

Equations as Functions Example: a.Solve y = 3x + 4 if the domain is {-2, -1, 0, 1}.

Equations as Functions Equations that represent functions can be written in functional notation, f(x). The symbol f(x) is read “f of x” and represents the value in the range that corresponds to the value of x in the domain. f(x) which is read “F of X” We can, and often do, let y= f(x) and we say “y is a function of x” DO NOT BE CONFUSED! f(x) DOES NOT MEAN f times x, or fx, f*x

Equations as Functions One can determine a functional value by substituting the given value for x into the equation. For example, if f(x) = 7x – 5 and x = 2, then f(2) = 7(2) – 5 or 9.