Consider the example of the states of the United States and the senators

Part I : Primary Task Response: Within the Discussion Board area, write up to 3 paragraphs that respond to the following questions with your thoughts, ideas, and comments. Be substantive and clear, and use examples to reinforce your ideas.

l. Consider the example of the states of the United States and the senators. You can say that the senators are not a function of the states because each state has more than one senator. However, you can say that the states are a function of the senators because each senator is associated with only one state.
a. make up your own examples of two real-world sets, with each set having more than one element.
b. discuss how elements of those sets can be paired.
c. explain whether one of the sets can be considered a function of the other.
2. Address the following regarding linear and nonlinear functions:
a. explain the difference between a linear and nonlinear function. Point out a specific type of nonlinear function to help explain the difference.
b. when solving the quadratic equation x2 - 8x + 12 = 0, the solutions are x = 2 and x = 6. If you examine the quadratic function by y = x2 - 8x + 12, how can you use the solution of the corresponding equation to determine the x - intercepts of the quadratic function?

Part II: Your Company would like to know how sales levels affect profits. If too few items are sold, then there is a loss..Even if too many items are sold, however, the company can lose money (likely because of low pricing)..It is good to know how many items can be sold for there to be profit. Functions are very useful in many areas, such as in business to find the profit an organization is making. For example, the following function expresses profit in terms of the number of phones sold by a particular company.

P(x) = x2 + 110x - 1,000
This function can be used to compute the profit (in thousands of dollars) from producing and selling a certain number, x, of thousands of smart phones.

a. compute the following: P(5), P(50), and P(120). Then, interpret the results.
b. graph the function using the desired graphing program. Paste the graph that you create into your assignment.
c.. discuss and interpret the meaning where the profit function crosses the x - axis. Also, discuss where the graph is above and below the x - axis, explaining what that means in terms of profitability. 
d. find the vertex of this function. What do the x-coordinate and y-coordinate of the vertex of this function represent?