For this portfolio, you will use your knowledge of functions to design a
roller coaster. You will draw a short roller coaster on graph paper, plot ordered
pairs on its path, and determine the slope, or rate of change, along the ride.
To design a roller coaster using functions, follow these steps:
1. Start by drawing a short roller coaster on graph paper. Be creative and design loops, hills, and twists as you like.
2. Label the x and y-axes on the graph paper. The x-axis represents the horizontal distance along the roller coaster, and the y-axis represents the height of the roller coaster.
3. Plot ordered pairs on the roller coaster's path. Choose points that represent the highest points, lowest points, loops, and any other significant features of the roller coaster. These points will help you determine the function for each section of the roller coaster.
4. Determine the slope, or rate of change, along the ride. To do this, calculate the difference in the y-coordinates (height) divided by the difference in the x-coordinates (distance) for each pair of consecutive points. This will give you the slope at each point.
5. Use the slope and any other information about the coaster's path to write equations for the sections of the roller coaster. For linear sections, where the slope is constant, the equation will be in the form y = mx + b, where m is the slope and b is the y-intercept. For nonlinear sections, you may need to use other types of functions, such as quadratic or exponential functions.
6. Test your equations by plugging in different x-values to see if they give you the corresponding y-values on the roller coaster's path.
7. Once you have equations for each section of the roller coaster, you can use them to answer questions about the roller coaster, such as finding the maximum height, minimum height, or the height at a specific distance along the coaster.
Remember that the design of a roller coaster involves both creativity and mathematical principles. Have fun with the design process and use your knowledge of functions to create an exciting and thrilling ride.