Session Long Project (Slp)

CASE ASSIGNMENT:

Exercises on Functions

1. Evaluate the function f(x) = 4x + 6 for x=-4.

2. Evaluate the function f(x) = 9x - 6 for x=3.

3. Take a look at the following table: x -2 -1 0 1 2 f(x) -5 -2 1 4 7

a. Write out an equation for f(x). Assume the function is linear.

b. What is the slope? Is it negative or positive? What information do we get from the slope?

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.

a. Write an equation for the number of boxes you sell as a function of the price you charge.

b. Denote "B" for number of boxes, and "P" for the price you charge.

c. Assume the function is linear..

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?

Assignment Expectations:

Differentiate between a function and a linear function.

Know the mathematical equation of a standard linear function.

Know how to compute the slope of a line. SESSION LONG PROJECT (SLP):

Sets (Part I)

1. List all the subsets of { 8, 16, 27, 31, 60}

2. Determine the number of subsets of {mom, dad, son, and daughter}

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?

4. Let U = {q, r, s, t, u, v, w, x, y, z}

A = {q, s, u, w, y}

B = {q, s, y, z}

C = {v, w, x, y, z}

Determine A ∩ (B ∪ C)

5. Use the Venn diagram to list the set of elements in roster form. Find A ∪ B.

Clearly define sets and set operations.

Select appropriate set elements and distinquish between sets, subsets, and proper subsets. Sets (Part II)

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).

Set A will be a list of all of these items.

Create Set B, from the items in Set A that you think are essential.

Create Set C, by taking the complement of Set B in Set A, i.e. all of the non-essential items.

Are sets B and C proper subsets of set A? Explain.

Submit a one to two page paper with this information along with Part I of SLP by the end of this module.

Identify a set and elements of the set that would make up subsets. from the original set.

Distinquish between improper and proper subsets. Required readings for SLP:

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:

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

Freedman, E. (1997). Professor Freeman's Math Help. Mathpower.com. Retrieved July 20, 2010, from: http://www.mathpower.com/anxtest.htm

After relieving at least a little bit of math anxiety, start digging into some material on sets and counting below:

Click here for a PowerPoint slide presentation on sets and counting.

Click here to read an excellent overview of sets and counting from the Stanford University:

Thomas Jech, (2002), Stanford Encyclopedia of Philosophy. Supplement to Set Theory. Basic Set Theory.

Retrieved November 13, 2010, from http://plato.stanford.edu/entries/set-theory/primer.html

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.

Retrieved November 13, 2010, from http://www.onlinemathlearning.com/math-sets.html

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.

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:

Click Here for a PowerPoint presentation that will introduce you to the basics of functions.

Required Readings:

Part I Function Basics

These links below are good introduction before looking at some of the more detailed tutorials.

Here is an simple but excellent Tutorial on Functions:

Stapel, E. (2004). Functions versus Reelations. Purple Math Practical Algebra Lessons. Retrieved July 20, 2010, from: http://www.purplemath.com/modules/fcns.htm

For a lively introduction to the topic, check out Definition of the Term Function from Zona Land:

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

What is a Function is also an excellent tutorial to introduce you to the basics:

Mueller, M. (n.d.). What is a Function. Exploring Precalculus. Retrieved July 20, 2010, from: http://www.wmueller.com/precalculus/functions/1.html

Part II Linear Functions

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:

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

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:

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

Here is another link from Zona Land on linear functions.

Zobel, E. (1997). Linear functions. Zona Land. Retrieved July 20, 2010, from: http://id.mind.net/~zona/mmts/functionInstitute/linearFunctions/linearFunctions.html