Project 2

Project 2 is designed to help you review the previous concepts (from the first three chapters) covered in the class. The project is due at the start of the final exam. No late projects will be accepted. You should be able to complete the questions denoted with the asterisks without the use of a calculator. Also, although no question(s) appear here you should be familiar with transformations and the different methods of solving a quadratic equation for the Final Exam. Here are the questions for Project 2:

pp. 160-2 #36^*, 38^*, 42^*, 50, 58^*, 64^*, 74, 80, 86^*, 104^*, 120^*;
pp. 242-5 #6^*, 78^*, 86^*, 94^*, 100^*, 128^*, 132^*, 138^*, 144^*, 146^*;
pp. 325-9 #8^*, 14^*, 36^*, 112^*, 128^*;
p. 382 # 28.

The questions must be completed in order. Each question is worth 1 point. All required steps must be shown and clearly written. You will receive either 0 points (not answered, not complete, not in order, not clearly written or not on the right track with finding the answer), 1 point (all steps are completely correct) or 0.5 points (all other cases) for each answer.

Thursday, 12 November 2009

There are several important announcements:

1. Test 4 is on Tuesday, 24 November 2009 and will cover at least Sections 2.6, 3.1, 3.2, 3.5, 3.6, 4.1, 4.2 and, maybe, 4.3 and 4.4;
2. Homework will not be collected next week;
3. There will be a quiz Tuesday (on Section 3.5, 3.6 or 4.1) and a quiz on Thursday.

Today, we completed several more examples from Sections 3.5 and 3.6. We discussed Section 4.1 (exponential functions). You should refresh your memory about transformations of functions, domain and range of functions, intervals of increase/decrease.

Next class, we will talk about logarithms. To get a head start on the concepts, you might want to start memorizing the definition and properties of logarithms. The following definition of logarithm is extremely important:

y = log_b(x) <=> x = b^y

Also, there are some properties of logarithms that we will discuss on Tuesday. Again, you may want to start memorizing them now. Here they are:

1. log_a(1) = 0
2. log_a(a) = 1
3. log_a(a^x) = x and a^log_a(x) = x
4. If log_a(x) = log_a(y), then x = y
5. log_a(x) = log_b(x)/log_b(a)
6. log_a(u*v) = log_a(u) + log_a(v)
7. log_a(u/v) = log_a(u) – log_a(v)
8. log_a(uⁿ) = n*log_a(u)

Homework for Sections 3.5, 3.6 and 4.1 will not be collected but you should be familiar with the questions:

• Section 3.5: #7-17, 23–26, 31, 33, 35, 37, 39
• Section 3.6: #1, 2, 6, 9–25, 27–30, 32, 33, 34, 36, 59–62, 65–68
• Section 4.1: #1–22, 27-36, 51-52

Tuesday, 3 November 2009

Quiz on Tuesday, 5 November and will cover two questions from Section 2.6.

Today, we covered a few additional problems from Section 2.6 both algebraically and graphically. Also, we started Sections 3.1 and 3.2. In these sections, we discussed the steps needed to sketch polynomial functions by hand:

1. find x-intercepts (see Sections 2.4 and 2.5 for refresher)
2. find y-intercept (see Section 1.4 for refresher)
3. identify long-term behavior (i.e., Leading Coefficient Test)
4. build table to identify additional points (see Section 1.4 for refresher)
5. (for quadratic functions only) find vertex

We will use these steps on Thursday to sketch graphs of a few polynomial functions. You should bring in graph paper to class (see http://www.printfreegraphpaper.com/).

The next homework assignment is due on Tuesday, 10 November 2009 and consists of:

Section 2.6*: # 7, 8, 11-27 odd**, 47, 51, 55, 59, 63, 67, 71, 73***, 75***, 77***
Section 3.1: # 1–6, 7–19 odd, 21, 23, 25, 27, 29–34, 45, 47
Section 3.2: # 1–9, 15–47 odd, 59–63 odd, 69–77 odd, 83–89 odd, 99– 107

NOTE: all graphs must be on graph paper.

* All solutions must be in interval notation.
** You do not need to graph solutions.
*** See Section 1.3 for refresher.

Thursday, 22 October 2009

 

Test 3 has been postponed to Thursday, 29 October 2009. and will cover Sections 1.5, 2.1, 2.2, 2.4 and 2.5 only.

 

Keep in mind, if you are asked to use a particular method to solve an equation, then you are expected to use that method. If you are only asked to solve, then you may use any method.

 

Today, we covered Section 2.5: Solving Other Type of Equations Algebraically. When solving these other types, you may still need to use one of the methods discussed in a previous section.

 

Even though homework assignments are typically due on Tuesdays, the next homework assignment is due on Thursday, 29 October 2009 (so that you can study from the assignment) and consists of the following:

Section 2.2: # 21, 25, 29, 33, 37, 41, 45, 49, 53, 65, 67, 69.
Section 2.4: # 23-65 odd
Section 2.5: # 1-11 odd, 15, 17, 19, 21, 23, 27, 31, 33, 35, 37, 39, 41, 43, 45, 49-59 odd

Tuesday, 20 October 2009

Important announcements:

Test 3 is scheduled for Tuesday, 27 October 2009;
Quiz is scheduled for Thursday, 22 October 2009 – I hinted that you should know how to solve a quadratic equation by completing the square by Thursday.

Today, we covered Section 2.4: Solving Quadratic Equations Algebraically using the following methods:

1. factoring and using the Zero Product Property
2. Square Root Theorem
3. Completing the Square
4. Quadratic formula
5. Graphing and finding x-intercepts

Here is a java applet to show the geometric reasons for the various steps in completing the square:
http://illuminations.nctm.org/ActivityDetail.aspx?ID=132.

Here is a webpage that has several examples of completing the square using the same steps that I have shown in class:
http://www.themathpage.com/alg/complete-the-square.htm.

Keep in mind, if you are asked to use a particular method to solve a quadratic, then you are expected to use that method. If you are only asked to solve, then you may use any method.

The next homework assignment is due on Tuesday, 27 October 2009 and consists of the following:

Section 2.2: # 21, 25, 29, 33, 37, 41, 45, 49, 53, 65, 67, 69.
Section 2.4: # 23-65 odd
Section 2.5*: # 1-11 odd, 15, 17, 19, 21, 23, 27, 31, 33, 35, 37, 39, 41, 43, 45, 49-59 odd
Section 2.6**: # 7, 8, 11-27 odd, 47, 51, 55, 59, 63, 67, 71, 73, 75, 77.

* Note: We have not completed any examples yet from this section. We will discuss them on Thursday.
** Note: The homework for this section may or may not be due – a decision will be made by Thursday.

Transformations of Functions Summary

Here is a good description of the various transformations of a function:

http://math.kennesaw.edu/~sellerme/sfehtml/classes/math1113/transformation.pdf.

Wednesday, 15 October 2009

Today, we covered Section 2.1 by looking at how to solve equations with denominators. We also previewed other sections from Chapter 2 by solving some other types of equations. Keep in mind, you are expected to know the following before starting Chapter 2:

1. How to factor expressions;
2. How to solve linear equations;
3. How to use the Square Root Theorem;
4. Evaluate the square of an expression inside a square root;
5. How to check your answers.

The next homework assignment is due on Tuesday, 20 October 2009 and consists of the following:

Section 1.5: # 21-25, 27-37, 47-52 (abd only);
Section 2.1: # 25-39 all, 41-44, 49.

Thursday, 1 October 2009

Important Announcements:

• There is no class on Tuesday, 6 October 2009
• Test 2 is on Thursday, 8 October 2009 and will cover the following:
  1. Finding domain of functions
  2. Odd and even functions (Section 1.4)
  3. Sections 1.6 and 1.7
• There are two corrections to the homework assignment that is listed below.

Today, we practiced a couple more examples of finding inverse functions and discussed how to evaluate an inverse function. The homework that is due on Thursday, 8 October 2009 is:

Section 1.7: # 59, 62, 63, 66, 68, 69, 71, 74, 75, 81-88, 93-102
Section 1.5*: # 21-37, 43, 44, 47, 48, 51, 52, 56

If you have any questions as you are preparing for Test 2, please email me (I will read my email frequently over the weekend) or see me during office hours.

Tuesday, 29 September 2009

There seems to be a problem with the pop-up announcements on iCollege. Thus, I will accept today’s homework on Thursday.

There will be a quiz on Thursday, 1 October 2009 and will cover inverse functions.

Test 2 is on Thursday, 8 October 2009 and will cover finding domains, even/odd functions (Section 1.4), Section 1.5, Section 1.6 and Section 1.7.

Today, we covered several examples of finding inverse functions. There are several ideas that you must make sure that you carefully consider when finding an inverse function:

1. f(x) must be 1-to-1 in order to be able to find the inverse. So, in step 1, you need to determine if f(x) is 1-to-1. To determine if f(x) is 1-to-1, graph and use the horizontal line test. If the function is not 1-to-1, then you must restrict the domain of f(x) so that if will have an inverse.

2. Check your answer. There are two ways to check: i. finding both f(f ^–1(x)) and f ^–1(f(x)) and checking that they both are equal to x; ii. graphing f(x), f ^–1(x) and y = x and checking that the graphs of f(x) and f ^–1(x) are mirror images over the y = x line. It is possible that you need to restrict the domain of f ^–1(x) to ensure the graphs of f(x) and f ^–1(x) are mirror images.

3. To graph a function with a restricted domain use the same idea that we used for piecewise-defined functions. For example, if we wanted to graph f(x) = x² – 6x + 9, x ≥ 3, then enter y1=(x^2-6x+9)(x≥3) into the TI83/84 and graph. To find the inequalities press 2nd key, then math key.

The next homework is due on Thursday, 8 October 2009 and will consist of the following:

Section 1.7: # 59, 62, 63, 66, 68, 69, 71, 74, 75, 81-88, 93-112
Section 1.5*: # 21-37, 43, 44, 47, 48, 51, 52, 56

* We will discuss Section 1.5 on Thursday, 1 October 2009.

Thursday, 24 September 2009

Important Announcement: Overwhelmingly, the class decided to move Test 2 to Thursday, 8 October. I will post the grades of the test in iCollege on the same day. The test will cover finding domain of functions, Sections 1.5, 1.6, 1.7 and maybe Section 2.1.

I will accept Project 1 on Tuesday, 29 September; however, I will deduct 5 points from the total.

The Quiz on Project 1 will be on Tuesday.

Today, we covered a few more examples of composition of functions. We discussed how to evaluate composition of functions using graphs of f(x) and g(x). We also talked about inverse functions: the compositions, f(f ^-1(x)) = f ^-1(f(x)) = x; the graphs of inverse functions are reflections over the y = x line; the steps to find the inverse function. We will finish Section 1.7 on Tuesday and finish Section 1.5 on Tuesday.

The next homework assignment is due on Tuesday, 29 September 2009 and will consist of the following:

Section 1.6: 61-70;
Section 1.7: 9, 12, 14, 15, 19, 21-24, 29, 34, 37, 39, 41, 43, 111-114

NOTE: If you have already completed some of these questions and submitted them today, then please do not re-do the questions – I will provide you with the appropriate credit.