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. If you are unsure about piecewise functions, or how to express them, this is a good time to do some independent research on their proper use and notation.

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. You may find it very useful to utilize graphing technology, such asGraph, to help you with this assignment

Q1

Research a favourite, or a famous, rollercoaster. Write a short summary of this coasters 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 as the initial drop of the rollercoaster you will be designing in this assignment will model the initial drop of this rollercoaster you have researched. Also remember to cite your sources.

Q2

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, 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.

Write a short paragraph describing what you foundand cite your sources.

Q3

Now it is time to create your own rollercoaster. Using the idea of piecewise functions, create an appropriate scale on your axes and design a rollercoaster, using technology likeGraph.You rollercoaster must have the features listed below. If you are unsure about piecewise functions, or how to express them, this is a good time to do some independent research on their proper use and notation.

You should try 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.

Not sure where to begin? Here is, that will help you understand how to set up and restrict the domain of functions inGraph.

Getting Started on this Assignment

Not sure where to begin? Take a look at the steps below to see how you can begin setting up the pieces of your rollercoaster usingGraph. Remember, this program can be downloaded for free here: https://www.padowan.dk/download/ , if you havent already done so.

1.Model Your Initial Drop.Begin this assignment by creating the functions that you have determined will model the initial drop of your rollercoaster. In the image below the initial pull and drop are modelled with a linear and a quadratic function.

2.Restrict the Domain.Now, by double clicking on one of the functions on the left hand side, you can restrict the domain of the function so that it begins and ends where you want.

In this example, the domain has been restricted to 0 x 6, producing a graph that looks like this:

3.Continue Restricting the Domain.Doing the same for the second function:

4.Create Your Piecewise Notation.This now models the initial drop of a rollercoaster, and you can continue adding pieces now until you have met all of the requirements of this assignment. To express these pieces as a whole using piecewise function notation, you can state it as:

Now it is time to create your own rollercoaster. Using the idea of piecewise functions, create an appropriate scale on your axes and design a rollercoaster, using technology likeGraph.You rollercoaster must have the features listed below. If you are unsure about piecewise functions, or how to express them, this is a good time to do some independent research on their proper use and notation.

You should try 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.

1. Uses at least four different polynomial functions, pieced together.
2. Models theinitial dropof the rollercoaster you researched.
3. Has at least 4 other drops.
4. Goes through an underground tunnel at least once (assumingy= 0 is the ground)
5. Any other features you feel would add to the ride and can be modelled with a polynomial function.

Q4

For each of the pieces in your design:

1. State the equation for the polynomial function used.
2. Determine the degree of the function.
3. State the domain and range of the restricted function.
4. Determine if the restricted function has even or odd symmetry, or neither. If neither, what transformations, if any, could be applied to make it even or odd?

Q5

Suppose you were asked to take thefirst three piecesof your rollercoaster and model them witha single function. Answer the following questions:

1. If you represent these three pieces with a single function, what degree do you think this function will be? Justify your reasoning.
2. Determine an equation for this function, using methods you have learned in the course so far. Refer to the module creating polynomial functions for examples of how to complete this question.
3. Graph the equation you created. How similar is it? If there are any differences, why do you believe that is?