Roller Coaster Design

Using at least three different functions and one inequality...$($must pick at least one rational function and one polynomial function$)$

Linear$/$Absolute Value Function

Rational Function

Sine and Cosine Functions

Logarithmic$/$Exponential

Polynomial Functions

Quadratic Function

Cubic Function

Quartic Function

Quintic Function

$...$design the frame of the world$$s most amazingly breathtakingly thrilling roller coaster on one set of axes. Let the x$-$axis represent horizontal distance from the starting point and the y$-$axis represent the height of your ride, relative to the ground, both in meters. Please ensure the height at the beginning of the ride corresponds to the height at the end of the ride.

Your assignment should utilize technology effectively. Use Desmos graphing calculator to design the frame of your rollercoaster. You can create an account using your school login ID$,$ and save your work directly online. Use a word processor, publisher, or presentation software to create your report. Be sure that you are using an equation editor to get presentable equations.$$

Part $1$ For each function $($each in a separate section$)$:

Identify the equation and type of three functions being used. Write the domain and range of the function used, the end behavior, and zeros, turning points and anything else worth noting. Give a brief explanation of each function including an explanation of how it helped with your design.

Include an inequality. $($Can be on the rollercoaster, in the name, the box of the ride$).$ Write the domain and range of the function, the end behavior, and zeros, and anything else worth noting.

State restrictions placed on the domain and range of the four functions and inequality to highlight the portion of the curve you are using for your ride.

Graph each function using Desmos Graphing Calculator and highlight the portion you are using for the ride.

Part $2$

At the end of your analysis of the four functions, you should graph all your functions $($with the restricted domains$)$ on one set of axes. Add some finishing touches to the rollercoaster. Give it a name and a ride description.

Communication: $($Weight $\mathrm{.}5)$

Criteria$$

Level $1$

Level $2$

Level $3$

Level $4$

Organization of Results

Poorly organized; difficult to follow.

Somewhat organized; lacks clarity or logical flow.

Well$-$organized; easy to follow with logical structure.

Exceptionally organized; clear and logical presentation.

Correct Notation

Incorrect or inconsistent notation.

Some correct notation; noticeable errors.

Consistently correct notation; minor errors.

Flawless use of correct notation.

Application: Includes $4$ functions and one inequality $($Weight $1)$

Half a mark for each: Domain, Range, End Behaviors, Zeros, # of Turning Points, graph of function

Function $1$: $/3$

Function $2$: $/3$

Function $3$: $/3$

$($Inequality$)$:$/3$

Each Function restricted correctly. Each restriction clearly highlighted on graph: $/2$

Example projects Below:$$

Copy of Roller$-$coaster Project

Copy of Roller Coaster Assignment