Math 4
Monday August 15th - Today we reviewed problem solving working in cooperative groups. Tonight's assignment is to complete a worksheet called "Some Review Algebra Problems". Selected Answers are listed below:
1. x = 24
3. This equation has no solutions.
4. x = 26/37
5. This equation has infinitely many solutions.
7. x = -4
9. This equation has 2 solutions: x = 0 or x = -1
10. This equation only has 1 solution: x = 1/3
12. This equation has 2 solutions: x = 6 or x = -2
14. This equation has 2 solutions: x = 2 or x = -7/4
15. This has 2 irrational solutions.
18. a = (2bh)/(b - 2h)
20. (5, 9)
22. (1, 2, 6)
24. x < 17/2
25. -6 < y < 7
I hope this helps. All answers will be given in class tomorrow. I look forward to seeing all of you again tomorrow!
Tuesday, August 16th - Students received their books today and continued to work on the algebra problems.
Wednesday, August 17th - We completed the algebra review and began the Function Review today. Tonight's assignment is to complete the algebra review (if needed) and to complete the function review. Selected answers to the function review are:
1. x e Reals and y < -1/4 (To find the vertex, either complete the square or use the x value of -b/(2a) to find the corresponding y value.)
2. x > 0 and y e Reals
3. Factor...
4. Let x = 0 to find the y-intercept and let y = 0 to find the x-intercept.
8. Consider A) how to find the vertices, B) where they are located and C) their appearance
10. h(1) + j(1) = 6 - 1 -2|1 - 5| = 5 - 8 = -3
13. This really means to multiply, so (f*g)(x) = (x - x2)(4x - 6) . Now foil this and write in descending powers of x.
14. This is composition, so (fog)(x) = (f(g(x)) = (4x - 6) - (4x - 6)2. Now expand this, collect like terms, etc.
16. To find an inverse of a function, switch x and y and solve for y.
18. Completing a square or using the quadratic formula might help in this case. Not all inverses will be functions... When will the inverse of a function be a function?
19. A(s) = s2 and s(p) = p/4. The independent variable in part C is p.
I hope this helps! See you tomorrow!
Thursday, August 18th - We continued the Function review by reviewing a variety of important definitions. The assignment is a function vocabulary review worksheet Selected answers are:
1. B) y > 0
C) [0, 1.5] U [3, infinity)
D) As x approaches infinity, y approaches infinity and as x approaches negative infinity, y approaches infinity.
E) (0, 0) and (3, 0)
F) Bounded below
G) (0, 0) and (3, 0) are absolute minimum values but (1.5, 2.25) is a relative maximum.
H) f(x) is neither even nor odd because f(-x) = |(-x)2 - 3(-x)| = |x2 + 3x| and that doesn't equal f(x) or -f(x).
I) It isn't one-to-one because f(0) = 0 and f(3) = 0 so each y value does not have a unique x value. It isn't onto because the range isn't all reals.
J) Let g(x) = |x| and let h(x) = x2 - 3x.
J (Again - Don't you hate these typos?) F(x) = -|(x + 2)2 - 3(x + 2)| + 5 = -|x2 + x - 2| + 5
2. f(x) = -3x/5 + 11/5
C) p(x) = 5x/3 -23/3
D) k-1(x) = -5x/3 + 11/3
3. f(x) and f-1(x) will be parallel whenever the slope is 1 or the slope is -1 (and then the function is its own inverse, so will they really be parallel?) f(x) and "f-1(x)" will be perpendicular when one function is parallel to the x-axis and the other graph is parallel to the y-axis - but then are they both functions...? So what should the answer to this question really be?
4. A) f(2) - g(2) = -4 - (-3) = -1
B) h(-2) + k(-2) = 3 + -1 = 2
C) f(g(-3)) = f(2) = -4 D) f(k(1)) = f(2) = -4
E) g-1(3) = -1 F) k-1(2) = 1 or 3??
G) f(x) is even because f(-x) = f(x) for all x.
H) g(x) and h(x) are 1-1 (one-to-one) because each y value has a unique x value.
I) f-1(-4) has 2 different values, so it really isn't a function.
j) g(x) and h(x) have inverses that are functions because they are 1-1.
k) k(x) = -|x - 2| + 3 (Change the vertex and reflect the graph.)
Enjoy!
Friday, August 19th- Quiz Review Today we continued reviewing wonderful properties of functions and received a "potpourri" of sample quiz problems. Coach Rinehimer has posted the answers to this worksheet on his blog, so feel free to look for the answers there. If you have any questions about any of them, I should be in early (7:45) Monday morning, so come on in and get all problems cleared up.
NovaNET: Week 1 and Getting Started!
Welcome!
Students who are eligible for NovaNET have failed a class and wish to recover credit by computer rather than face to face instruction with a teacher in a traditional classroom setting. While this delivery is not for everyone, thoughtfully reflect on your personal motivation and desire to succeed. If your counselor is willing to schedule NovaNET for you, the following documents are required before you can start your online work.
1.Counselor Placement Checklist
2.Contract
3.Student Transcript
4.Syllabus Acknowledgement
The checklist, contract, and syllabus acknowledgement must be complete with signatures and all required information. The transcript is mandatory for record-keeping, schedule verification, and other matter that may arise during the semester.
The NovaNET lab is open from 7:45 a.m. until 8:15 for extra time daily. No afterschool time is available. Students must work diligently from bell-to-bell on a daily basis. As the instructor has lunch duty, no students may work during lunch. Careful attention to staying in class, on track to finish the course on time is imperative in planning for successful credit recovery. NovaNET is a priviledge; use it well as seats are at a premium and priority is given to Seniors with two courses to complete.
Attendance is imperative as there is no 'make-up' time for NovaNET. Time missed is simply time that cannot be repeated. The student must be responsible for being in class to complete work under teacher supervision, as the program is not available or valid in any other location than the NovaNET lab.
