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, 4.3 and, maybe 4.4;
2. Homework will not be collected next week;
3. There will be a quiz Tuesday (on Section 4.1) and a quiz on Thursday.

Today, we discussed Section 4.1 (exponential functions) and started Section 4.2 (logarithmic functions). Remember that the logarithm function is the inverse function of exponential functions. You should refresh your memory about transformations of functions, domain and range of functions, intervals of increase/decrease

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. 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 finding vertex of a quadratic.

Today, we covered most of 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 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.

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, 2.5 and 2.6 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. We also started Section 2.6: Solving Inequalities Algebraically and Graphically. We will cover more from Section 2.6 on Tuesday. 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 2.4: # 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 all methods yet from this section. We will discuss the other methods on Tuesday.

Tuesday, 20 October 2009

Important announcements:

Test 3 is scheduled for Tuesday, 27 October 2009;
Quiz is scheduled for Thursday, 22 October 2009.

Today, we started to discuss Section 2.5: Solving Other Types of Equations Algebraically. Specifically, we solved several equations involving radicals. Keep in mind, you must check your answer(s) either by graphing or by placing the answers into x of the original equation. Also, you will need to use other methods of solving equations (i.e., methods discussed in other sections).

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, including graphing.

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

Section 2.4: # 23-65 odd
Section 2.5*: # 1-11 odd, 15-45 odd, 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 all methods yet from this section. We will discuss the other methods on Thursday.
** Note: We have not completed any examples yet from this section. We will discuss them on 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.

Thursday, 15 October 2009

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

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, 20 October 2009 and consists of the following:

Section 2.1: # 25-39 all, 41-44, 49;
Section 2.2: # 21, 25, 29, 33, 37, 41, 45, 49, 53, 65, 67, 69.

The homework assignment due the following week (i.e, due on Tuesday, 27 October 2009 – the day for Test 3) will consist of the following:

Section 2.4: # 23-65 odd
Section 2.5: # 1-11 odd, 15-45 odd, 49-59 odd
Section 2.6: # 7, 8, 11-27 odd, 47, 51, 55, 59, 63, 67, 71, 73, 75, 77.

Tuesday, 30 September 2009

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

Test 2 is on Thursday, 1 October 2009 and will cover finding domains, even/odd functions (Section 1.4), 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

Thursday, 24 September 2009

Important Announcement: Test 1 is on Thursday, 1 October. 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. 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, 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.

Tuesday, 23 September 2009

Project 1 is due on Thursday. We will have a quiz based on Project 1 on Thursday.

Today, we completed another set of examples of arithmetic combinations of functions as well as evaluating these combinations for specific values of x. We only started two examples of compositions of functions – we will discuss more on Thursday. Keep in mind, I will use a different notation for combinations as follows:

The text uses (f ⎄ g)(x); I will use f(g(x));

The text uses (g⎄ f)(x); I will use g(f(x)).

As promised in class, I have cut down on the number of questions in the homework that is due on Thursday. It will now consist of the following:

Section 1.6: # 5-26, 31-38, 55-60.