High School

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Draw a graph of a roller coaster with the following guidelines:

- Let the x-axis represent time (t) in seconds and the y-axis represent height (h) in feet.
- The roller coaster must operate for 60 seconds or more (t ≥ 60).
- The height of the roller coaster should be lower than 456 feet (h < 456).

Include at least one instance of each of the following six functions. You may use other functions if desired:

1. Linear function
2. Absolute Value function
3. Quadratic Function
4. Square Root Function
5. Cube Root Function
6. Cubic Function

Answer :

Final answer:

A graph of a roller coaster is to be drawn, with the x-axis as time in seconds and the y-axis as height in feet. The roller coaster graph will feature linear, absolute value, quadratic, square root, cube root, and cubic functions, which all represent different sections of the ride, reflecting the diversity in the roller coaster's path.

Explanation:

The task involves drawing a graph of a roller coaster with specific guidelines. The x-axis will represent time (t) in seconds, and the y-axis will represent height (h) in feet. The roller coaster's duration should be at least 60 seconds, and its maximum height should not exceed 456 feet. The graph will incorporate at least six different types of functions: linear, absolute value, quadratic, square root, cube root, and cubic functions. Each function represents a different segment of the roller coaster's path, emulating the various slopes and curves one would experience on a real roller coaster ride.

A linear function could represent a constant slope, either ascending or descending. An absolute value function could simulate a sharp peak or valley where the coaster quickly changes direction. The quadratic function might illustrate a parabolic arc, either upwards or downwards. The square root function can be used for a gradually increasing slope, while a cube root function could represent a section that initially changes slowly before steepening. A cubic function can show various rates of acceleration or deceleration throughout a segment of the ride. Each function should be connected in a way that makes physical sense for a roller coaster, ensuring the flow from one to the next is smooth.

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