In Modules Four and Five, we studied the properties of functions, such as determining whether they are increasing or decreasing, and finding their maxima, minima, and concavity. We then put all of that together to sketch what the graph of the function looks like.

In this discussion, we do the opposite. We start with what we want the graph of a function to look like and then try to find a function that has those properties. This type of problem is useful in design when we have a target end result (shape of the curve) and need to find a way to build something (a function) that leads to that target result. For example, this could be used in noise reduction where engineers remove static from sound.

You are required to post one initial post and to follow up with at least two response posts for each discussion assignment. You should post your discussion response first, and then respond to other students.

For your initial post (1), you must do the following:

• Before posting in this discussion, go to the 6-1 Module Six Discussion: Finding a Function to Match a Shape activity in Mobius. There you will be given certain properties that we want a function to have (increasing, decreasing, local maxima, etc.), and you need to find a function that has all of those properties. You can test out your solution with the graphing program in the Mobius Module Six discussion activity.
• In the Brightspace discussion, post the criteria that you needed to match and the function that you found in Mobius. Describe the process that you used to solve the problem in Mobius.
• Complete your initial post by Thursday at 11:59 p.m. of your local time zone.

For your response posts (2), you must do the following:

• Comment on other classmates' analyses and their equivalent versions. Compare and contrast your approach to solving the problem to how your classmates solved it.
• Reply to at least two different classmates outside of your own initial post thread.
• Complete the two response posts by Sunday at 11:59 p.m. of your local time zone.
• Demonstrate more depth and thought than simply stating that "I agree" or "You are wrong." Guidance is provided for you in each discussion prompt.

To complete this assignment, review the Module Six Discussion Guidelines and Rubric.

Please note: Grading and feedback will be provided for this assignment in Brightspace using the Module Six Discussion Rubric.