Relations and Functions

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1. Relations and Functions

   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 theexampleto complete this discussion:

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

     If the last letter of your last name is	On pages 708 – 711, solve the following problems
     A or B	22 and 30
     C or D	24 and 32
     E or F	26 and 34
     G or H	28 and 36
     I or J	12 and 46
     K or L	14 and 48
     M or N	16 and 50
     O or P	18 and 52
     Q or R	20 and 54
     S or T	2 and 56
     U or V	4 and 58
     W or X	6 and 60
     Y or Z	8 and 64

   • 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. Useboldfont 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

   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.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.

Assignment
To complete the following quiz, go to this week’sAssignmentlink in the left navigation.

Composition and Inverse

Read the following instructions to complete this assignment:

1. We define the following functions:
   
   • Compute(f–h)(4).
   • Evaluate the following two compositions:
     A:
     B:
   • Graph the g(x) function and transform it so that the graph is moved 6 units to the right and 7 units down.
   • Find the inverse functions:
     C:
     D:.
2. Write a two- to three-page paper (not including the title page) that is formatted in APA style and according to theMath Writing Guide. Format your math work as shown in theexample, and be concise in your reasoning. In the body of your essay, do the following:
   • Demonstrate your solution to the above problems, making sure to include all mathematical work as well as explanations for each step.

For information regarding APA samples and tutorials, visit the Ashford Writing Center, within the Learning Resources tab on the left navigation toolbar.