Project Assignment THE LIBRARY OF FUNCTIONS AND PIECEWISE DEFINED FUNCTIONS

Prof. Laura Galindo | MAC 1105 | 07/05/2018

PAGE 1

Graph the lateral view of a roller coaster track using functions from The Library of Functions from your textbook and merging them by means of a piecewise defined

function.

PROJECT GUIDELINES:

? The project is to be done in groups of up to three students.

? Use at least 4 different functions from the library. You may use one type of function more than once.

? Use Desmos to graph the chosen functions.

? The x-axis must represent the distance from the starting point and the y-axis must represent height (The scaling of the each axis must be realistic in feet or meters).

? Combine all the chosen functions into one piecewise defined function (Hint: Use transformations to move the functions from the library on the coordinate plane).

? There should be no gaps between the functions that make the different pieces. This means that the value of each function at the end of each piece must equal the value of the following function at the beginning of the next piece.

? All angles between function should be at least 120 degrees.

STUDENTS MUST TURN IN:

? A print out of the graph obtained in Desmos; showing the lateral view of the roller coaster track and the equations, on the left hand side, that were used. It might be better to take a screen shoot.

? A short paragraph where you describe the process you went through to do your roller coaster track.

? The answers to the following questions (Print a word document containing the paragraph and the 5 answers):

1. What does the domain of your piecewise defined function represent? 2. What does the range of your piecewise defined function represent? 3. Does your function have relative or absolute maximum or minimum values? At

which values of x do they occur? What do they represent? 4. Can your roller coaster have loops? Why? 5. What would you do to add a loop to your roller coaster? Can this new roller

coaster be represented by a function?

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EXAMPLE 1 (units are in meters)

EXAMPLE 2 (units are in meters)

Answer the following question for understanding (Do not hand them in):

? About how high each track takes you.

? Which of the two example you think is more thrilling?

? How far from the starting point did the tracks take you?

? How could you find the points where each function ends and begins?

HAVE FUNA print out of the graph obtained in Desmos; showing the lateral view of the roller coaster track and the equations, on the left hand side, that were used. It might be better to take a screen shoot. ˆ’ A short paragraph where you describe the process you went through to do your roller coaster track. ˆ’ The answers to the following questions (Print a word document containing the paragraph and the 5 answers): 1. What does the domain of your piecewise defined function represent? 2. What does the range of your piecewise defined function represent? 3. Does your function have relative or absolute maximum or minimum values? At which values of x do they occur? What do they represent? 4. Can your roller coaster have loops? Why? 5. What would you do to add a loop to your roller coaster? Can this new roller coaster be represented by a function?