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Work 3 thru 5 and Letters

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Week 3 Discussion 1

In this discussion, you will simplify and compare equivalent expressions written both in radical form and with rational (fractional) exponents. Read the following instructions in order and view the

example

to complete this discussion:

S or T

54 and 100

54. 100.

· Simplify each expression using the rules of exponents and examine the steps you are taking.

· Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.):

· Principal root

· Product rule

· Quotient rule

· Reciprocal

· nth root

Refer to

Inserting Math Symbols

for guidance with formatting. Be aware that with regards to the square root symbol, you will notice that it only shows the front part of a radical and not the top bar. Thus, it is impossible to tell how much of an expression is included in the radical itself unless you use parenthesis. For example, if we have √12 + 9 it is not enough for us to know if the 9 is under the radical with the 12 or not. Thus we must specify whether we mean it to say √(12) + 9 or √(12 + 9). As there is a big difference between the two, this distinction is important in your notation.
Another solution is to type the letters “sqrt” in place of the radical and use parenthesis to indicate how much is included in the radical as described in the second method above. The example above would appear as either “sqrt(12) + 9” or “sqrt(12 + 9)” depending on what we needed it to say.

Your initial post should be at least 250 words in length. Support your claims with examples from required material(s) and/or other scholarly resources, and properly cite any references. Respond to at least two of your classmates’ posts by Day 7.

Week 3 Assignment

Real World Radical Formulas
Read the following instructions in order to complete this assignment:

1. Solve parts a and b of problem 103 on page 605 and problem 104 on page 606 of Elementary and Intermediate Algebra.

2. Write a two to three page paper that is formatted in APA style and according to the

Math Writing Guide

. Format your math work as shown in the

example

and be concise in your reasoning. In the body of your essay, please make sure to include:

· An explanation of what the parts of the formula mean before using it to get your answers. Study the Instructor Guidance examples to learn how to solve the formula for another variable.

· Your solution to the above problems, making sure to include all mathematical work.

· A discussion of how and why these concepts are important in the “real world.” Describe another situation that could be evaluated using these concepts.

The paper must be at least two pages in length and formatted according to APA style. Cite your resources in text and on the reference page. For information regarding APA samples and tutorials, visit the Ashford Writing Center, within the Learning Resources tab on the left navigation toolbar.

Carefully review the

Grading Rubric

for the criteria that will be used to evaluate your assignment.

Week 4 Discussion 1

In this discussion, you will solve quadratic equations by two main methods: factoring and using the Quadratic Formula. Read the following instructions in order and view the
example
to complete this discussion:

· Find the problems assigned to you in the table below.

If the third letter of your last name is	On page 636, solve the following problem by factoring	Solve the following problem by using the Quadratic Formula
A or L	46	48 on p. 646

46. 48.

· For the factoring problem, be sure you show all steps to the factoring and solving. Show a check of your solutions back into the original equation.

· For the Quadratic Formula problem, be sure that you use readable notation while you are working the computational steps. Refer to

Inserting Math Symbols

for guidance with formatting.

· Present your final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required.

· Incorporate the following four math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):

· Quadratic formula

· Factoring

· Completing the square

· Discriminant

Week 4 Assignment

Real World Quadratic Functions
Read the following instructions in order to complete this assignment:

1. Solve problem 56 on pages 666-667 of Elementary and Intermediate Algebra.

2. Write a two to three page paper that is formatted in APA style and according to the
Math Writing Guide
. Format your math work as shown in the
example
and be concise in your reasoning. In the body of your essay, please make sure to include:

· An explanation of the basic shape and location of the graph and what it tells us about the Profit function.

· Your solutions (it is a double question) to the above problem, making sure to include all mathematical work for both problems.

· Discuss how and why this is important for managers to know, and explain what could happen if the ideal conditions were not met.

Week 5 Discussion 1

In this discussion, you will be assigned two equations with which you will then do a variety of math work having to do with mathematical functions. Read the following instructions in order and view the
example
to complete this discussion:

· Find your two equations in the list below based on the last letter of your last name.

K or L

14 and 48

14. f(x) = | x − 2 | 48.  x = 1 − y2

There are many ways to go about solving math problems. For this assignment you will be required to do some work that will not be included in the discussion. First, you need to graph your functions so you can clearly describe the graphs in your discussion. Your graph itself is not required in your post, although the discussion of the graph is required. Make sure you have at least five points for each equation to graph. Show all math work for finding the points.

· Specifically mention any key points on the graphs, including intercepts, vertex, or start/end points. (Points with decimal values need not be listed, as they might be found in a square root function. Stick to integer value points.)

· Discuss the general shape and location of each of your graphs.

· State the domain and range for each of your equations. Write them in interval notation.

· State whether each of the equations is a function or not giving your reasons for the answer.

· Select one of your graphs and assume it has been shifted three units upward and four units to the left. Discuss how this transformation affects the equation by rewriting the equation to incorporate those numbers.

· Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.):

· Function

· Relation

· Domain

· Range

· Transformation

Week 5 Assignment

Composition and Inverse
Read the following instructions in order to complete this assignment:

1. We define the following functions:

· Compute (f – h)(4).

· Evaluate the following two compositions: and .

· Transform the g(x) function so that the graph is moved 6 units to the right and 7 units down.

· Find the inverse functions and .

· Your solutions to the above problems, making sure to include all mathematical work for both problems, as well as explaining each step.

· A discussion of the applicability of functions to the real world, based upon your reading of Chapter 11 of Elementary and Intermediate Algebra. Be sure to use specific examples, a brief discussion of why your examples are important, and to cite your sources.

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