The function which represents the modified design of the roller coaster is Y = 2f(0.15x²-10x+C).
What define a function?
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Here, the function: Y = 2f(0.3x - 1) + 10
Therefore, to transform the function
We have to compare with a general function and integrate.
g(x) = f(bx + c).
We now integrate to transform the function which gives us
Y = (2f) integral {0.3x - 1} + 10
Y = 2f { 0.15x² - x } + 10x + c
Y = 2f(0.15x²-10x+C)
Modified design of roller coaster is
Y = 2f(0.15x²-10x+C)
Thus, the function which represents the modified design of the roller coaster is Y = 2f(0.15x²-10x+C).
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