# Death Coster

## Written Report:

In the height versus time graph that was constructed, the minimum amount of functions needed in this assignment was exceeded to make the rollercoaster as appealing, mathematically and visually, as possible. Each function had restrictions upon them in order to connect smoothly with each other. With the help of the domain and range tools in Desmos, we restricted each graph to effortlessly connect the beginning and end of each function. We started off with an exponential function because it would have matched the reality of the beginning of any rollercoaster most efficiently. We limited at a certain height and time by restricting its domain and range in order to connect to a linear function. The linear function was cut off at a point where the quadratic could connect to create a dramatic drop. Next, a period of a negative cosine function was created to assist the passengers upwards where a polynomial cubic function further carried them to the major drop in the roller coaster that reached 300ft which was created by a sine function. The sine graph connected to the quadratic which linked to a rational function that started to descend the passengers. The rational function extended until it met the log function, which ended the graph with a smooth finish. This fulfilled the time requirement of one-hundred seconds.

## Summary...

The creation of the rollercoaster was quite easily done because the group had made a rough sketch of how they wanted to arrange their functions. The members had arranged the required functions according to how they wanted the roller coaster to look, something that had drops and showed intensity. Uniqueness and the mandatory requirements were kept in mind when the sketch was being drawn. The drops were added in places where suitable functions would support them. They were mainly what composed the roller coaster. The shape was adapted primarily through how the rollercoaster elevated and then made its way down. An issue which occurred were gaps between the function. The group had difficulty connecting the functions together which meant that most time was spent to get the correct restriction to be placed. To create a rollercoaster that had a visual representation of something that would exist in real life, was also difficult because the restrictions would not play out as the group wanted it. Due to this, the students decided to add more functions to the coaster. Overall, the project was done in time and the individuals played all their roles with their full capability.

250 ft:
12 ft:

## Calculate Average Rate of Change For...

10 to 15 seconds:
50 to 60 seconds:

35 seconds: