Piecewise Functions Project Roller Coaster PDF

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Summary

Sample project for an intervention to target the needs of diverse learners of functions in middle school Mathematics....

Description

Name:

Date: Roller Coaster Project - Investigate Piecewise Functions

Congratulcitions! You’ve graduated college as a Physics & Mathematics double major, and you’ve scored your dream job working at Six Flags to help them design new roller coasters. In the graph below, you will see that your boss has started developing the plan for a new roller coaster - THE TIGER - but needs you to finish the job. Answer the questions below based on the given piecewise function and the graph that is attached. Given: The function f(x) will model the roller coaster’s height from the ground in feet over time, measured in seconds since the ride started.

r

5(2)‘, —5x 2 -I— 40a, 35, 80,

2.5x — 22.5, —15x + 380, 5,

0 x< 4 4< x< 7 7< < 9 9 x < 12 12 x < 15 15 < x < 17 17 < x < 23 23 z < 25 25 ext 27

A & C D E F G H

Part I: Graphing 1) Graph the boundary lines for this function on the provided graph paper. 2) Based on the graph provided, use points on the line to determine the function for Part E.

3) Based on the graph provided, determine the function for Part F.

4) Gi aph parts A, B, C, D, G, H, and I on the graph paper.

Part II: Analysis 5) How many seconds does the roller coaster last?

6) What is the roller coaster’s starting height? How many seconds does it take the roller coaster to reach maximum height?

7) Describe what the roller coaster is doing in the interval 7 < x < 9.

8) Use your knowledge of function notation and piecewise functions to determine the following: a. f(10) = i. Explain what this value means in real world context.

b. f(20) = i. Explain what this value means in real world context.

c. If 16 seconds have passed since the roller coaster started, what is the height of the roller coaster?

Bonus: When does the roller coaster reach 100 feet above the ground?

Roller Coaster Project - Extension:

We just got a report that the best roller coasters in the world reach a maximum height of 100 feet. Our roller coaster only reaches a maximum height of 80 feet. Your boss has asked you to propose a redesign for The Tiger in which it now reaches a maximum of 100 feet. How could we redesign the graph such that the maximum height reaches to 100 feet? How would you need to alter the function f(x) to model this newly designed roller coaster? Have fun, and good lucid!!

Date:

Name:

Roller Coaster Project - Investigate Piecewise Functions

Congratulations! You’ve graduated college as a Physics & Mathematics double major, and you’ve scored your dream job working at Six Flags to help them design new roller coasters. In the graph below, you will see that your hoss has started developing the plan for a new roller coaster - THE TIGER - but needs you to fi‘nish the job. Answer the questions below based on the given piecewise function and the graph that is attached. Given: The function f(x) will model the roller coaster’s height from the ground in feet over time, measured in seconds since the ride started.

5(2)‘, —5x* + 40a, 35, 2 —5(x — 12) -1- 80, 'N '• 'w “â1 O , 2.5x — 22.5, —15x + 380, 5,

0 x< 4 4 x...