Question

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 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.

f(x)=5(2), 0≤x<4 a -5x2 + 40x, 4≤x<7 b 35, 7≤x<9 c -5(x – 12)2 + 80, 9≤x<12 d __________, 12Vx<15 e __________, 15≤x<17 f 2.5x-22.5, 17≤x<23 g -15x+380, 23≤x<25 h 5, 25≤x<27

graph the boundary lines for this function on the provided graph paper

Answer 1

Graphing the boundary lines for a piecewise function of a roller coaster's height requires plotting each segment over its specified interval, ensuring continuity and feasibility in the roller coaster's design.

Step-by-step explanation:

The task requires completing the design of a new roller coaster by analyzing a piecewise function, which is incomplete in the given description. To graph the boundary lines for this function, one would plot the distinct pieces of the function over their respective intervals on provided graph paper.

The intervals given define sections of the roller coaster's height over time, and the function changes form depending on the value of x, which represents time in seconds since the ride started.

For example, for the interval 0≤x<4, we have a constant height of 5 feet. The boundary lines for the rest of the intervals would be plotted similarly, following the equations provided for each section. When plotting a curve like -5x2 + 40x, for instance, this would represent a parabolic trajectory of the roller coaster's movement, illustrating a change in height with respect to time.

For the intervals where no function is provided, such as segments d and e, additional specifications or context would be required to complete the task. It is important to note the continuity of the function at the transition points between segments to ensure the roller coaster's design is physically feasible.