In a certain state, the maximum speed permitted on freeways is 65 mi/h, and the minimum is 40 mi/h. The fine F for violating these limits is $15 for every mile above the maximum or below the minimum. A. Complete the expressions in the following piecewise-defined function, where x is the speed at which you are driving. For each of the three blanks, write a rule. Make sure to indicate which rule you are selecting for each part of the domain. if 0 65 B. Find F(30), F(50), and F(75) Evaluate the piecewise function for each value in the function after the rules have been created. C. What do your answers in part b) represent? Explain the meaning of each of the answers obtained in the context of the freeway permitted speed and the tickets received for driving outside of the allowed speed interval. D. Which rule was the most challenging to write? Why? What do you think might be the rule that most students may get wrong? Why? Explain which rule kept you thinking longer or challenged you in any way. Identify what was challenging and describe which rule you think the majority of students may struggle with and what part of the problem makes it challenging