8. Engineering a rollercoaster 

In this assignment you only need to do questions four and five. 

Question 4 

For each of the pieces in your design:

Question 4 options:

a) State the equation for the polynomial function used.

b) Determine the degree of the function.

c) State the domain and range of the restricted function.

d) Determine if each unrestricted function pieces have even or odd symmetry, or neither. If neither, determine which transformations, if any, could be applied to make it even or odd over its unrestricted domain?

Question 5

Suppose you were asked to take the first three pieces of your rollercoaster and model them with a single function. Answer the following questions:

Question 5 options:

a) If you represent these three pieces with a single function, what degree do you think this function will be? Justify your reasoning.

b) Determine an equation for this function. You can refer to the module Creating Polynomial Functions for examples of how to complete this question or use a more trial-and-error approach.

c) Graph the equation you created together with the first three functions. How similar is it? If there are any differences, why do you believe that is?