<p> CASE ASSIGNMENT:</p><p>Exercises on Functions</p><p>1. Evaluate the function f(x) = 4x + 6 for x=-4.</p><p>2. Evaluate the function f(x) = 9x - 6 for x=3.</p><p>3. Take a look at the following table: x -2 -1 0 1 2 f(x) -5 -2 1 4 7</p><p> a. Write out an equation for f(x). Assume the function is linear.</p><p> b. What is the slope? Is it negative or positive? What information do we get from the slope?</p><p>4. Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 250 boxes. But when you raise your price to $4 you only sell 120 boxes. </p><p> a. Write an equation for the number of boxes you sell as a function of the price you charge. </p><p> b. Denote "B" for number of boxes, and "P" for the price you charge.</p><p> c. Assume the function is linear.. </p><p>5. A reservation clerk worked 12.6 hours one day. She spent twice as much time entering new reservations as she did verifying old ones and one and a half as much time calling to confirm reservations as verifying old ones. How much time did she spend entering new reservations? </p><p>Assignment Expectations:</p><p>Differentiate between a function and a linear function.</p><p>Know the mathematical equation of a standard linear function.</p><p>Know how to compute the slope of a line. SESSION LONG PROJECT (SLP):</p><p>Sets (Part I)</p><p>1. List all the subsets of { 8, 16, 27, 31, 60} </p><p>2. Determine the number of subsets of {mom, dad, son, and daughter}</p><p>3. At MegaSalad, a salad can be ordered with some, all, or none of the following set of ingredients on top of the salad greens: {ham, turkey, chicken, tomato, feta cheese, cheddar cheese, cucumbers, onions, red peppers, hot peppers }. How many different variations are there for ordering a salad? </p><p>4. Let U = {q, r, s, t, u, v, w, x, y, z}</p><p>A = {q, s, u, w, y}</p><p>B = {q, s, y, z}</p><p>C = {v, w, x, y, z}</p><p>Determine A ∩ (B ∪ C) </p><p>5. Use the Venn diagram to list the set of elements in roster form. Find A ∪ B.</p><p>Assignment Expectations:</p><p>Clearly define sets and set operations.</p><p>Select appropriate set elements and distinquish between sets, subsets, and proper subsets. Sets (Part II)</p><p>Also, for the first SLP I want you to put into practice what you have learned about sets and functions. I want you to create three sets, set A, set B, and set C by going through the items you use at work (or in your field). </p><p>Set A will be a list of all of these items. </p><p>Create Set B, from the items in Set A that you think are essential. </p><p>Create Set C, by taking the complement of Set B in Set A, i.e. all of the non-essential items.</p><p>Are sets B and C proper subsets of set A? Explain.</p><p>Submit a one to two page paper with this information along with Part I of SLP by the end of this module.</p><p>Assignment Expectations: </p><p>Identify a set and elements of the set that would make up subsets. from the original set.</p><p>Distinquish between improper and proper subsets. Required readings for SLP:</p><p>For the vast majority of you who have not had any math since high school, I suggest that before you delve into this class you first read these:</p><p>Annonymous, (n.d.). Ten Ways to Reduce Math Anxiety. Accessed July 20, 2010, at: http://larc.asp.radford.edu/ten_ways_to_reduce_math_anxiety.asp</p><p>Freedman, E. (1997). Professor Freeman's Math Help. Mathpower.com. Retrieved July 20, 2010, from: http://www.mathpower.com/anxtest.htm</p><p>After relieving at least a little bit of math anxiety, start digging into some material on sets and counting below:</p><p>Click here for a PowerPoint slide presentation on sets and counting.</p><p>Click here to read an excellent overview of sets and counting from the Stanford University:</p><p>Thomas Jech, (2002), Stanford Encyclopedia of Philosophy. Supplement to Set Theory. Basic Set Theory.</p><p>Retrieved November 13, 2010, from http://plato.stanford.edu/entries/set-theory/primer.html</p><p>Now take a look at online math learning another great site on sets by clicking on these Tutorial on Sets: onlinemathlearning.com, (2008). Math: Sets & Set Theory.</p><p>Retrieved November 13, 2010, from http://www.onlinemathlearning.com/math-sets.html</p><p>If you are confused by the math symbols take a look at this web site, it provides a good explanation of the most commonly used symbols.</p><p>Math Symbols: The Most Valuable and Important Symbols Used, Accessed July 20, 2010, at: http://www.solving-math-problems.com/math-symbols.html#Operations Background Reading for Case Assignment:</p><p>Click Here for a PowerPoint presentation that will introduce you to the basics of functions. </p><p>Required Readings:</p><p>Part I Function Basics </p><p>These links below are good introduction before looking at some of the more detailed tutorials.</p><p>Here is an simple but excellent Tutorial on Functions:</p><p>Stapel, E. (2004). Functions versus Reelations. Purple Math Practical Algebra Lessons. Retrieved July 20, 2010, from: http://www.purplemath.com/modules/fcns.htm</p><p>For a lively introduction to the topic, check out Definition of the Term Function from Zona Land:</p><p>Zobel, E. (1997). Definition of the Term Function. Zona Land. Retrieved July 20, 2010, from: http://id.mind.net/~zona/mmts/functionInstitute/definitionOfFunction/definitionOfFunction.html</p><p>What is a Function is also an excellent tutorial to introduce you to the basics:</p><p>Mueller, M. (n.d.). What is a Function. Exploring Precalculus. Retrieved July 20, 2010, from: http://www.wmueller.com/precalculus/functions/1.html</p><p>Part II Linear Functions </p><p>Hofstra has a good Tutorial on Linear Functions. Their Chapter 1 summary is a good overview, and also has some material on linear functions. The self quizzes are worth going through as well, they are linked through these pages below:</p><p>Warner, S. & Costenoble, S.R. (2000). 1.3 Linear Functions. Finite Mathematics and Applied Calculus. Retrieved July 20, 2010, from: http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorialsf0/frames1_3.html Warner, S. & Costenoble, S.R. (2000). Summary of Chapter 1. Finite Mathematics and Applied Calculus. Retrieved July 20, 2010, from: http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/Summary1.html</p><p>These tutorials called "Linear Functions and Slope" have lots of practice problems with solutions. If you go through these tutorials you will gain a solid understanding of the material:</p><p>Annenberg Media. (1997) Linear functions and slope. Learning Math. Retrieved July 20, 2010, from: http://www.learner.org/channel/courses/learningmath/algebra/session5/index.html</p><p>Here is another link from Zona Land on linear functions.</p><p>Zobel, E. (1997). Linear functions. Zona Land. Retrieved July 20, 2010, from: http://id.mind.net/~zona/mmts/functionInstitute/linearFunctions/linearFunctions.html</p>