Instructions You can either copy and paste these questions into a word document, or use the "Print Assignment" button to print a hard copy for yourself. Then complete these assignment questions by hand, or in your word processor, and upload your full solutions to the Dropbox. Print Assignment Your task in this assignment is to use polynomial functions to design a rollercoaster. To express your rollercoaster design you will create a piecewise function out of the polynomial functions. Your rollercoaster must meet certain criteria, and the questions below will guide you through this process. In the end, you will submit a written assignment, showing all of your calculations and ideas, to the dropbox. You can, and may find it very useful to, utilize graphing technology, such as Graph, to help you with this assignment. Question 1 (1 point) an [3 Research a favourite, or a famous, rollercoaster. In your own words, write a short summary (2-3 paragraphs) of this coaster's general information; include its name, a picture, where it is located, when it was built, why you picked it and its physical characteristics. Make sure you note the height of the initial drop of the rollercoaster you have researched. The initial drop of the rollercoaster you will be designing in this assignment will model the same initial drop as the rollercoaster you have researched. Also remember to cite your sources (1-2 sources). Question 2 (1 point) an C] It may be useful now to do a little bit of research on the physics of rollercoasters. You will not need to do any physics-style calculations in this assignment, but you will be expected to abide by the common rules. For example, a rollercoaster cannot be expected to defy gravity after the initial drop; it must be given momentum at the beginning of the track, and cannot reach as high a height at the end of its track as it can at the beginning. Also, it must run on a smoothly curving, connected track. In your own words, write a short paragraph describing what you found and cite your sources (1-2 sources). Question 3 (1 point) Now it is time to create your own rollercoaster. Requirements: . The first thing you should do is define your variables for each axis, including units of measure, and create an appropriate scale on your axes. - Use piecewise functions and technology (like Graph) to design your rollercoaster - it needs to be precise, so these graphs will not be hand-drawn. If you are unsure about piecewise functions, or how to express them, review the lesson pages about this topic in the unit. . Your rollercoaster must be realistic: designed with common physics principles. . You must aim to make each of the polynomial functions flow into one another to create a smooth ride for your passengers. - To prevent your functions from overlapping, make sure to restrict the domain of the function. - Set each polynomial function to a different colour and submit a picture (or a screen capture) of your design, as well as the piecewise function notation that models it. - Have no less than 4 and no more than 8 polynomial functions in your piecewise design. Not sure where to begin? Here is a Getting Started Guide that will help you understand how to set up and restrict the domain of functions in Graph. You may also use Desmos for this assignment. Make sure that your rollercoaster model also has the following features. Features: C] 3) Uses at least four different polynomial functions, pieced together. 0 b) Models the initial drop of the rollercoaster you researched. O c) Has at least 4 other drops. [3 d) Goes through an underground tunnel at least once (assuming y= 0 is the ground) C] e) Any other features you feel would add to the ride and can be modelled with a polynomial function. Question 4 (1 point) For the following, make sure that you keep your information organized and concise (within two pages). It should be easy to follow, and should showcase your understanding of polynomial functions, so show your steps/reasoning. For each of the pieces in you r(piecewise) design: C] a) State the equation for the polynomial function used. [3 b) Determine the degree of the polynomial function. 0 c) State the domain and range of the restricted function piece. D d) Assuming that each function piece was unrestricted, for each, determine whether the function piece has 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 (1 point) an Suppose you were asked to take the first three pieces of your rollercoaster and model them as closely as you can with a single polynomial function. Answer the following questions: Q a) If you represent these three pieces with a single function, what degree do you think this function will be? Justify your reasoning. O b) Determine an equation for this function. You can refer to the Creating Polynomial Functions lesson pages for help. D c) Graph the single function you created with the first three functions of your model together on the same grid. How similar is your single function compared to the first three pieces of your model? If there are any differences, why do you believe that is? Explain. Submitting Your Assignment This is the end of your assignment. After completing all of the questions, upload your work to the appropriate dropbox. Print Assignment