The Final Exam is scheduled for Tuesday, 13 Dec 2005, 5:45 p.m. - 7:45 p.m. I will be available starting from approximately 4:30 p.m. You can come early to start the final exam (so you can take your time answering the questions) or to ask me questions. Please email me anytime prior to Monday if you have any questions.

The cumulative (i.e., everything we discussed during the semester could be included) final exam will consist of 12 multiple choice questions and 15 short answer questions. Please bring a scantron (the green form no. 882-E) and a #2 pencil. There may be questions on the final exam on which you may not use a calculator. I will provide graph paper.

The Math Lab will be having an Exam Jam for College Algebra on Monday, 12 December from 6:00 p.m. to 8:00 p.m.

Here is the correlation between Test IV questions and homework, assignments and quizzes: http://gpc.edu/~jweber/math1111/math1111test4corrHw.htm.

Most of the test will be non-calculator-based. The only section for which you may be able to use a calculator is section 3.1 (for graphing functions of the form:
f(x) = ax² + bx + b.).

Today we finished section 4.2 and discussed most of section 4.4. Thus, Test 4 will cover sections 2.6, 2.7, 3.1, 3.2, 3.6, 4.1, 4.2, 4.4 (only the concepts that we covered in section 4.4) and transformations of functions.

Assignment #3 was collected. If necessary, you can hand it in on Monday (I will deduct 2 points). I do not accept make-up quizzes late.

Today's quiz was a take-home quiz. If you were absent, then email me for a copy of the quiz.

IMPORTANT: Please bring a #2 pencil to class on Wednesday, 30 November 2005. You will need it to fill out the course evaluation forms.

Today we finished section 4.1; we graphed a few more exponential functions; we discussed compound interest and continuous interest; practiced several interest problems. We also discussed transformations of exponential functions.

We started section 4.2 (logarithm functions). We discussed the definition and how to convert between exponential form and logarithm form. We still need to discuss how to graph logarithm functions.

Assignment #3 is due on Wednesday, 30 November 2005.

Test 4 is on 5 December 2005. It will cover sections 2.6, 2.7, 3.1, 3.2, 3.6, 4.1, 4.2, 4.3 (possibly 4.4) and transformations of functions.

We completed sections 3.2 and 3.6. We started section 4.1 - to graph exponential functions, make a t-chart of x and y values and plot the points (see Example 2 on p. 376 of your textbook). All sketches should be completed on graph paper (download at: http://www.mathematicshelpcentral.com/graph_paper/files/Form5A-BW.pdf).

Here is a list of the current due dates:

• Assignment 2 is due on Monday, 28 November 2005;
• Quiz 20 is due on Monday, 28 November 2005 (make sure that you draw the graphs on graph paper;
• Assignment 3 is due on Wednesday, 30 November 2005;
• Test IV will be on Monday, 5 December 2005;

I hope you have a happy and safe Thanksgiving break.

Instructional Support Services tutorial center will be closed for the Thanksgiving holidays.

We will stop tutoring at 2:00 pm on Wednesday November 23.

Tutoring will begin again on Sunday November 27 at 1:00pm.

IMPORTANT: Test IV will be moved to Monday, 5 December 2005.

We finished discussing section 3.1 – how to graph quadratic functions of the form: f(x) = ax² + bx + c. Here are the steps:

1. find the direction which the parabola opens;
   • if a > 0, then the parabola opens upward; if a < 0, then the parabola opens downward;
   • the vertex of the parabola is at the point (h, k) - note that if the parabola opens upward (a > 0), then the vertex is the local minimum and if the parabola opens downward (a < 0), then the vertex is the local maximum.
     
     
2. find the vertex and plot the point;
   • To find the x-coordinate of the vertex use: x = –b/(2a). To find the y-coordinate of the vertex find: f(x) where x is the x-coordinate of the vertex found previously.
     
     
3. find the x-intercept(s) and plot the point(s), if they exist: set y = 0 and solve for x. Note that you will need to know the various methods for solving quadratics that we discussed in section 1.5. Remember, if the results are complex numbers, then there are NO x-intercepts.
   
   
4. find the y-intercept and plot the point: set x = 0 and solve for y. Note that when the quadratic is written in this form (i.e., f(x) = ax² + bx + c), then y-intercept = c.
   
   
5. sketch the curve through the points.
   
   

We started section 3.2. The discussion wan on determining whether a function is a polynomial function and on the long-term behavior of a polynomial function. The general form of a polynomial function is f(x) = a_nxⁿ + a_n-1x^n-1 + &ctdots; + a₂x² + a₁x + a₀, where a_n ≠ 0 and n is a positive integer or zero. The long-term behavior of the graph of a polynomial function is determined by the largest power of x (i.e., the leading term, a_n). There are four possibilities we need to consider: when a_n is positive and negative; when n is even and odd. Here are the four possibilities:

	an is positive	an is negative
n is even	up to right up to left	down to right down to left
n is odd	up to right down to left	down to right up to left

The quiz for today was a take-home quiz. The extra credit portion is worth 10 points and is NOT required. This assignment and the extra credit is due on Monday, 26 November 2005.

Remember: Test corrections are due on Monday, 21 November 2005. You can receive up to 1/2 additional credit. Please follow the instructions on http://gpc.edu/~jweber/testCorrections2.htm. NOTE: For this test correction you do NOT have to write a strategy to prevent similar errors on future tests.

We discussed section 2.7. The main ideas are:

• Find the inverse of a function. The steps are:
  1. check if f(x) has an inverse (graph and use horizontal line test);
  2. change notation from f(x) to y;
  3. switch the x and y (all other parts of the equation remain in the same location);
  4. solve for y;
  5. change notation from y to f ^-1(x);
  6. check using the compositions of f(f ^-1(x)) and f ^-1(f(x)) (the result of both compositions MUST be x).
     
     
• the graphs of f(x) and f^–1(x) are reflections over the y = x line. In other words, if the point (2, 5) is on the graph of f(x), then the point (5, 2) is on the graph of f ^-1(x).

We discussed most of section 3.1. Here are the main ideas:

• the standard form of the equation of a quadratic function is: f(x) = a(x – h)² + k. We can find some information about the graph of the quadratic from this equation:
  • if a > 0, then the parabola opens upward; if a < 0, then the parabola opens downward;
  • the vertex of the parabola is at the point (h, k) - note that if the parabola opens upward (a > 0), then the vertex is the local minimum and if the parabola opens downward (a < 0), then the vertex is the local maximum.
    
    
• We can graph the quadratic WITHOUT a calculator! Here are the steps:
  1. find the direction which the parabola opens;
  2. find the vertex and plot the point;
  3. find the x-intercept(s) and plot the point(s), if they exist: set y = 0 and solve for x. Note that you will need to know the various methods for solving quadratics that we discussed in section 1.5. Remember, if the results are complex numbers, then there are NO x-intercepts.
  4. find the y-intercept and plot the point: set x = 0 and solve for y. Note that there will ALWAYS be one and only one y-intercept.
  5. sketch the curve through the points.

The quiz for today was a take-home quiz. You are permitted to receive assistance on the quiz.

Test III was returned today. Test corrections are due on Monday, 21 November 2005. Please follow the instructions on http://gpc.edu/~jweber/testCorrections2.htm. NOTE: For this test correction you do NOT have to write a strategy to prevent similar errors on future tests.

Here are the classes:

MONDAY – WEDNESDAY

CRN	CLASS	TIME	TEACHER
33419	COMM 1201-549	5:15 - 6:45	SIMMONS
33420	POLS 1101-549	5:15 - 6:45	HAMMOND
34545	PSYC 1101-549	7:00 - 8:30	STAFF
34510	MATH 0098-573	7:00 - 9:00	WATERS

TUESDAY – THURSDAY

CRN	CLASS	TIME	TEACHER
30808	ARTS 1301-549	5:15 - 6:45	FARLEY
33423	MATH 1111-573	5:15 - 6:45	RANDALL
34470	HIST 2112-549	7:00 - 8:30	REEVES
34438	ENGL 1102-549	7:00 - 8:30	STAFF

Test 3.

The worksheet on transformations was due today. If you did not hand in the worksheet, then you can hand it in on Monday – you will lose two points in credit.

There will be a quiz on Monday on transformations of functions.

We finished section 2.6 and briefly started section 2.7.

Test III is on Wednesday, 9 November 2005. It will covers sections 2.1, 2.3, 2.4, 2.5 and 2.6. Keep in mind that there will be two parts to the test: part one will consist of questions on transformations of functions (section 2.5) - NO calculator will be allowed for this section; part two will consist of questions on the other topics. You will need to complete and submit part one before you start part two.

If you have any questions while you're preparing for the test, please don't hesitate to email me.

The transformations worksheet is due on Wednesday, 9 November 2005. IMPORTANT NOTE: All I require for the worksheet are the graphs (ON graph paper - http://www.mathematicshelpcentral.com/graph_paper/files/Form5A-BW.pdf) of the functions using the appropriate transformations of f(x) = 1/x or f(x) = 1/x²!

We finished section 2.5. For additional assistance on transformations of functions, complete the following worksheet that I typically provide my algebra/pre-calculus students: http://gpc.edu/%7Ejweber/math1113/sect0205notes.htm and/or read over my notes for transformations (see http://gpc.edu/%7Ejweber/math1113/sect0205notes.xml).

Make sure that you are familiar with the "rules" for transformations. You should start memorizing them - check your textbook or the link to my notes above for the correct rules.

The quiz on Monday will NOT be on transformations of functions.

I distributed a worksheet on graphing using transformations. You are required to graph, by hand, the functions f(x) = 1/x and f(x) = 1/x². Then you are to graph the four circled functions using the appropriate transformations. You are to graph these on graph paper (see http://www.mathematicshelpcentral.com/graph_paper/files/Form5A-BW.pdf for graph paper). This assignment is worth 10 points and is due on Wednesday, 9 November 2005. You may receive any assistance that will help you understand and correctly graph the functions.

Note that the transformation question(s) on Test III will be non-calculator based so it will be better if you complete the worksheet without a calculator (you may check your solution with the calculator for the worksheet, but will not have this opportunity on the test).

We started and completed most of section 2.5. We still have to cover compositions of functions and finding domain of the composition of functions.

We finished section 2.4. We started section 2.5: Transformation of functions. For additional assistance on transformations, complete the following worksheet that I typically provide my algebra/pre-calculus students: http://gpc.edu/%7Ejweber/math1113/sect0205notes.htm.

The quiz on Wednesday will NOT be on transformations of functions.

We will finish chapter 2 on Wednesday.

GA Perimeter College District Wellness Dept. is sponsoring flu vaccinations for students, employees and community. Here are the dates, times and locations:

• Clarkston Campus; Wed., November 2nd, 11-2pm; Library Rotunda; $20
• Decatur Campus; Wed., November 2nd, 10-2pm; Student Center; $20
• Rockdale Center; Mon., November 7th, 11:30-2pm; Bldg A; $30 (First 20 students FREE)
• Dunwoody Campus; Wed., November 16th, 11-2pm; Student Center-Alcove; $20 (First 20 students FREE)
• Gwinnett University Ctr; Mon., November 14th, 11:30-1:30pm; Student Center; $30

For more information call 678.891.3391

We discussed how to find domain and range of functions. We have previously discussed how to find domains of functions algebraically. Today, we showed how to find the range of the function graphically. In a later section, we will discuss how to find the range of a function algebraically.

We also discussed finding the local maximum and local minimum of functions. The directions for using the TI-83/84 are located at: http://gpc.edu/%7Ejweber/math1113/ti83_fnMax.htm.

Lastly, the answer to quiz 13 can be found at: http://gpc.edu/~jweber/math1111/quiz13soln.xml.

The answer to tonite's quiz is: http://gpc.edu/~jweber/math1111/quiz12soln.xml.

We covered how to evaluate and graph piecewise-defined functions. We have completed section 2.3

We started (one example) of finding domain and range of functions (section 2.4). We'll cover more domain and range; finish section 2.4; and cover section 2.5.

We discussed two more difference quotient questions. When finding the difference quotient of a rational function (i.e., a fraction with a function in numerator and denominator), you will need to find a common denominator to be able to subtract two rational functions.

We also discussed several more domain questions. Keep in mind the following:

1. when given a rational function, you can replace the numerator with a 1 only if the numerator does not contain an even root – this will help when graphing the function on the calculator.
2. when given a rational function that contains an even root:
   1. find a 'temporary' answer for your domain using the even root; then
   2. find the values of x that makes the denominator zero; then
   3. remove the number(s) found in step 2 from the interval found in step 1.

Lastly, we discussed whether equations are functions or not. To determine if an equation is a function: solve the equation for y, graph the function and use the vertical line test. If there are two or more y terms, then switch the x and y, solve the equation for y, graph the function and use the horizontal line test.

Please prepare for Monday's class by reviewing how to graph piecewise-defined functions on the TI-83 (see http://gpc.edu/%7Ejweber/math1113/ti83_pdf.htm) and bring some graph paper (download from http://www.mathematicshelpcentral.com/graph_paper/files/Form5A-BW.pdf).

Remember that test corrections are due on Monday. If you have any questions, please email me.

We covered finding domain of functions. I discussed the concepts of restrictions on domains. There are two restrictions that we have discussed so far:

1. denominators cannot be zero;
2. the argument of an even root cannot be negative.

We also discussed the difference quotient. I will provide 1-2 more examples in the next class.

Test 2 was returned. Test corrections are due Monday, 20 October 2005. Make sure that you follow the directions (see http://gpc.edu/~jweber/testCorrections2.htm).

Question number 2 was worth 10 points; all other questions were 9 points. A very common error was not checking your work.

The Advising & Counseling Services is hosting a seminar for Pre-Pharmacy Majors! Find out all the details for a smooth transition and successful admission to Pharmacy School! Representatives from UGA College of Pharmacy and Mercer University will be talking about their admissions programs. They will also have information on the South University program.

Wednesday, October 19
1:00 PM - 2:30 PM
Room A-1630

Students from all campuses are welcome to attend.

Friday, 14 Oct 2005 is the Fall Midpoint for Full Term Classes. If you intend to withdrawal from the course with a W you need to do so by this date. Otherwise, if you withdrawal after this date you will receive a WF.

We finished section 2.1 and started section 2.3

Test 2 in on Monday, 10 October 2005. It will cover sections 1.5, 1.6, 1.7, 2.1, 2.3 (you are only responsible for evaluating functions in section 2.3). Another teacher will supervise the test. NOTE: If you have any questions prior to the test, please email me - I will answer them as soon as I am able to read and respond to your email.

There will be NO quiz on Wednesday, 12 October 2005. There will be a substitute that will cover additional concepts from section 2.3.

We finished section 1.7 and started section 2.1

The step-by-step answer to today's quiz is located at http://gpc.edu/~jweber/math1111/quiz9soln.xml.

Test 2 is on Monday, 10 October 2005. It will cover sections 1.5, 1.6, 1.7, 2.1, 2.3 and possibly 2.4. Another teacher will supervise the test.

I started posting instructions on how to use the TI-83/84 calculators: http://gpc.edu/~jweber/math1111/ti83instructions1111.htm.

We finished section 1.6. We cover most of section 1.7 (we still need to cover absolute value inequalities in section 1.7). On Monday, we will finish section 1.7 and cover sections 2.1 and 2.2.

We discussed solving equations with rational (i.e., fractions) exponents by using substitution. Here is the shortcut method for the substitution:

• Solve for x: 3x^2/5 – 16x^1/5 + 5 = 0
1. Make an explicit substitution statement: let t = x^1/5
   always let your new variable be equal to the x with the smaller exponent. Note, the coefficient is NOT included in the subsitution.
2. Rewrite the equation with the new variable: 3t² – 16t + 5 = 0
   Anywhere you see x^1/5 in the original equation, replace it with t. Also, we will replace 3x^2/5 with 3t². Note that the exponent of t when substituting for this term is the numerator of the original fraction in the exponent.
3. This 'new' equation is a quadratic equation. Solve using any method that we learned from section 1.5. Using the quadratic formula: t = 5, 1/3. Note that the answer at this point is in terms of t. We were asked to solve for x.
4. Get answer in terms of x by using substitution equation from step 1 and placing the values from the previous step into t and solving for x:
   • t = x^1/5 implies 5 = x^1/5 implies (5)⁵ = (x^1/5)⁵ implies x = 3125
   • t = x^1/5 implies 1/3 = x^1/5 implies (1/3)⁵ = (x^1/5)⁵ implies x = 1/243
5. Thus, x = 3125, 1/243. Check both answers using any method for checking. Both are solutions.

Here is the step-by-step solution to quiz #6.

We covered how to solve and check square root equations with two square roots. There are at least two 'methods' to solve these equations:

1. keep both square roots on the same side of the equals sign; or
2. keep both square roots on opposite sides of the equals sign.

There are at least two methods to check using the calculator (always use the original equation when checking):

1. Type the left side of the equals sign as Y1 and the right side of the equals sign as Y2, then graph to find the intersection. The advantage here is the speed at which you can check your answer. However, the disadvantage is at the end of one of the graphs - if the end of one graph appears not to intersect the other graph, they may, in fact, still intersect! This is a shortcoming of most graphing programs. In addition, you may use the intersect function of your calculator.
2. Type the left side of the equals sign as Y1 and the right side of the equals sign as Y2. Exit from the graphing editor by typing 2^nd, then MODE. Find the variable Y1 by typing VARS, then right arrow, then 1, then type into parentheses one of your solutions (e.g., you should have Y1(2)). Hit enter to execute. Do the same with Y2. If the values are equal, then this is a valid solution. Repeat with second solution.

One test 1, most of the students did not check #7 with the calculator. HINT: use the graphing method.

I handed out the test corrections instructions. The test corrections are due on Wedensday, 28 September 2005. Recall that I siad that I will give 1/2 the credit back for test 1. You should start working on the corrections now. If you have any questions or want to make sure that you are performing the required work, please email me or let me review your work on Monday.

Test 1.

I will have the graded tests available on Wednesday. I will returen the tests during the LAST 15 minutes. The tests will include your current overall average. Lastly, I will explain the procedure for test corrections.

We started section 1.6. We will finish section 1.6 on Wednesday, 21 September 2005.

Test 1 is on Monday, 19 September 2005 and will cover sections 1.2, 1.3, 1.5 and 1.6. Regarding section 1.6, you are only responsible for solving equations that contain only one (1) square root.

The test consists of 14 questions. These questions have a similiar format to the previous tests provided on the website (http://gpc.edu/~jweber/math1111/Tests/math1111Tests.htm). Here is some important information:

• I will read my email every couple of hours over the weekend. If you have ANY questions, please do not hesitate to email me.
• There are some links on the webpage that discuss how to study for math tests and how to overcome math anxiety. You may want to read some of these if you think it will be helpful (http://gpc.edu/~jweber/math1111/miscTopics.html).
• You may start the test as early as 5:00 p.m. You MUST start the test NO LATER THAN 5:45 p.m. You may work on the test until 8:30, if needed. Don't pressure yourself about the time.
• You are required to show work for ALL questions. You are NOT required to show ALL steps. However, if your answer is not correct, then I will give partial credit on the basis of how many correct steps are provided.
• If I ask you to solve a quadratic equation using a specific method, then you MUST use that method. If you don't use that required method, then you will NOT receive any credit. If you are not asked to use a specific method, then you may use any method that you want to use.
• You may use your calculator to check your work.
• You should NOT leave any question blank. You should ALWAYS try something. If you don't know a question, then remember that you will have an opportunity to make test corrections for additional credit (http://gpc.edu/~jweber/testCorrections2.htm).

We finished section 1.5. We will cover section 1.6 on Wednesday.

Test 1 is on Monday, 19 September 2005 and will cover sections 1.2, 1.3, 1.5 and 1.6.

We discussed section 1.5 concerning the various methods to solve a quadratic equation of the form ax² + bx + c = 0:

1. quadratic formula;
2. graphically (i.e., graphing y = ax² + bx + c on the calculator and finding where the graph crosses the x-axis);
3. factoring and using the zero-product property;
4. square root theorem;
5. completing the square.

For the first three methods, make sure that you have the equation in standard form: ax² + bx + c = 0. The the last two methods, use the form: ax² + bx = –c.

You should be familiar with all these methods. Test 1 will have some questions that ask you to use a particular method - you MUST use the method to receive ANY credit. There will be some questions that will aske you to solve, but will not suggest a method. For these latter questions, you may use any method that you would prefer to use.

We will practice more of solving these equations during Monday's class.

We finished covering section 1.2. You should be knowledgeable of all concepts and homework questions in this section.

I have updated the Missed Test/Quiz Policy in the syllabus (see http://gpc.edu/~jweber/math1111/math1111Fa05Syl.htm) . This section now states:

Only ONE make-up test (for any of the first three tests) is permitted for extreme extenuating circumstances. The make-up test MUST be taken within ONE week of the original test. NO test corrections will be permitted for make-up tests. The next missed test will be the drop test. Any other missed test will be given a grade of zero. No make-up quizzes will be given for ANY reason.

The test correction policy can be found at: http://gpc.edu/~jweber/testCorrections2.htm.

I have uploaded the 'notes' for the first four sections. They include:

• Knowledge Prerequisites - the prior knowledge you will need to use for the new concepts in the section; and
• Learning Goals - what you are expected to know AFTER we cover the section in class.

1. declarative knowledge - the definitions of the concepts;
2. procedural knowledge - how to perform the steps in order to answer the questions in the section; and
3. conditional knowledge - the "why" questions.

I will also include (as time permits): Questions to Ponder, Purpose of this Section, and General Notes.


You should read the section notes prior to class!

We covered problems #10, 20 and 24 from section 1.2 in class. Although these are problems you are expected to know, I started with these to make sure that everyone is at the same starting point. We also showed two different ways to check your answer. One method is by graphing each side the equal sign as separate functions on your calculator and find the point of intersection. It is IMPORTANT that you find the answer ALGEBRAICALLY, then CHECK your answer on the calculator. On a test or quiz, I EXPECT to see the algebra (you need not show all steps, but you need to show enough steps so that I can recognize that you know how to solve the problem algebraically).

The quiz on Monday will be a similar to the problems listed above. We will cover the rest of section 1.2 on Monday along with sections 1.3 and 1.4.

We covered the syllabus (see http://gpc.edu/~jweber/math1111/math1111Fa05Syl.htm) for the course. You are responsible to be completely familiar with the details of the syllabus.

I also showed the various items that are included in (and discussed items that will be added to) the class website (see http://gpc.edu/~jweber/math1111/math1111.htm).