Unit 1 : Honors Precalculus

1. Unit 1: Honors Precalculus • Lesson 1: Standard 1.1 and 1.2 (1-1, 1-2) • Lesson 2: Standard 1.3 (1-3, 1-4) • Lesson 3: Standard 1.3 and 1.4 (1-5, 1-7) • Lesson 4: Standard 1.3 (1-6) • Lesson 5: Standard 1.6 (1-8, 2-6) • Lesson 6: Standard 1.5 (2-1, 2-2)

2. Welcome to Precalculus!Mrs. Bunting Room C109 • Get an index card and your handouts. • Pick up a textbook (Rust with spiral on front) • Find your seat on the seating chart and take your seat. Fill out your index card. • Please begin to work on reviewing the material in Section 1-1 of your book. • Use your textbook and tablemates to help yourself review this material. • You will need to TAKE NOTES on the material. • Completep 10 #17 – 37 odd, 41-47 all

3. Standard 1.1: distinguish between relations and functions, identify domain and range, and evaluate functions (Section 1-1)p 10 #17 – 37 odd, 41-47 all By the time you and your group finish you will answer… • What is a relation? • What is contained in the domain of a relation? In the range? • What is a function and how is it different from a relation? • What is the vertical line test and what is it used for? • What does function notation look like? • How are functions evaluated for specific values?

4. What is Honors Precalculus? • You will be introduced to: • Higher level algebra skills! • Common and Natural Logarithms! • Limits! • Arithmetic, Geometric and Infinite Series! • Polynomial, Rational and Exponential Functions! • Lots of Trigonometry! • Rectangular and Polar Coordinates! not necessarily in that order…

5. What Can I Expect? • We will cover at least a section a day. • We will complete a unit pretty much weekly. • Each quarter will have several portfolio projects. • You can expect to have Precalculus work to do every single night.

6. Grading to Standards: • In a nutshell: • 1. You need to master EVERYstandard to pass. • 2. Any standard which you do not pass must be reassessed. • To Do Well: • 1. Complete your homework. It is your ticket to reassess. • 2. Reassess promptly while things are fresh.

7. Extra Help • Tutorial – right here in C109! Everyday but Tuesday (Library Duty) • Got Math? • 3C in C211 Ms Kielkucki • 3D in C106 Ms Ciliano • 4C in C104 Mr. Lisella • 4C in C100 Ms Rohrer • 4D in C100 Ms Bunting

8. Unit 1: “Get in Line” In this unit we will complete… • Standard 1.1: distinguish between relations and functions, identify domain and range, and evaluate functions (1-1) • Standard 1.2: perform operations (add, subtract, multiply, divide, compose) on functions (1-2) • Standard 1.3: analyze graphs and make predictions based on linear functions (1-3, 1-4, 1-5, 1-6) • Standard 1.4: graph and interpret piecewise functions (1-7) • Standard 1.5: solve systems of equations (2-1, 2-2) • Standard 1.6: solve systems of linear inequalities (1-8, 2-6)

9. Standard 1.1 (continued): Using the Vertical Line Test and Stating The Domain From A Graph (1-1) y y x x

10. y y x x

11. Standard 1.1: Finding the Domainof a Function in Equation Form (1-1) To find out what the independent (x) values for a function will be involves finding out what they cannot be. There are TWOBozo No-No’s: No values which cause zero’s in denominators No values which cause a negative under a square root (or any even root)

12. Find the values for x which are not in the domain of the function, then state the domain in proper set notation.

13. Find the values for x which are not in the domain of the function, then state the domain in proper set notation.

14. Find the values for x which are not in the domain of the function, then state the domain in proper set notation.

15. Find the values for x which are not in the domain of the function, then state the domain in proper set notation.

16. Standard 1.2: perform operations (add, subtract, multiply, divide, compose) on functions (1-2) When we finish this lesson you will be able to … Perform basic math operations with functions Create, use and check composite functions

17. Given: Add the functions: Written: It means:

18. Given: Subtract the functions: Written: It means:

19. Given: • Multiply the functions: • Written: • It means:

20. Given: Multiply the functions: Written: It means:

21. You try it… Given:

22. Composite Functions: Careful with notation, this is not multiplication. It means you actually put one function into the other. The second one is going into the first.

23. Example:

24. Example:

25. To Check:

26. Homework: • For Tomorrow: • HW 1.1: p 10 #17 – 47 odd, 48-50 all • HW 1.2: p 17 #11 – 23 odd, 31 • By Monday: • Cover book • Get your binder or notebook setup • Get parental form turned in

27. P 25 #41 Have your homework out to be checked! Warm-Up:

28. Homework:

29. Standard 1.3: analyze graphs and make predictions based on linear functions (1-3,1-4) At the end of this lesson you will be able to… • Identify and properly use the three forms of linear equations • Find x- and y-intercepts • Define, identify and use the formula for slope • Identify the two special cases of slope

30. Linear Functions • What does a linear equation look like? • Are all the equations of lines also functions? • How many of the forms do you remember?

31. Standard Form:

32. Standard Form: • Where A, B and C are numbers like this. • In this form you can tell what about the line? • Nothing.

33. Slope-Intercept Form • Where m is… • And b is… • In this form you can… • Tell exactly what the line looks like • Graph the line

34. Point-Slope Form: • Used to develop the linear equation if you know the slope, m, and one point on the graph, (x1, y1). • Find the standard form of the equation of the line which has a slope of -1 and passes through the point (-4, 5).

35. What if you only have two points on the graph? • Find the standard form of the equation which passes through the points (6,5) and (4,-5). • Find slope. • Use slope and one of the points to find equation of the line.

36. Graph a couple…

37. The Two Special Cases of Slope:

38. Finding the Zero of a Linear Function: • Zero is another name for the x-intercept. You will also hear it called a root. • The y-intercept is called b but not much else.

39. Finding x- and y-intercepts:

40. Homework: • HW1 1.3: P24 #13 – 33 every other odd • HW2 1.3: P30 #11 – 27 every other odd

41. Warm-up:

42. Homework:

43. Standard 1.3: analyze graphs and make predictions based on linear functions (1-5) By the end of this lesson we will be able to answer… • How can parallel and perpendicular lines be identified from their equations? • How can the properties of lines be used to identify geometric figures? • How can the coefficient for an equation be found so that it will be parallel or perpendicular to a specific line?

44. Parallel and Perpendicular Lines Parallel lines have the same slope Perpendicular lines have slopes which are negative reciprocals of each other. Find the equation of the line parallel to the equation above and passing through (2,-2) Find the equation of the line perpendicular to the equation above and passing through (-4,1)

45. Special Case: Lines which have the same slopeand the same y-intercept are called coinciding.

46. Slope and Distance: Consider the polygon with vertices at (0,0), (1,3), (3,-1) and (4,2). Is it a parallelogram? Is it a rectangle?

47. Are these lines parallel, coinciding perpendicular or none of these? neither parallel coinciding perpendicular

48. Solving for an unknown coefficient:

49. Solving for an unknown coefficient:

50. Standard 1-4:graph and interpret piecewise functions (1-7) In this lesson we will … • Identify piecewise functions including greatest integer, step and absolute value. • Graph piecewise functions.