The above rollercoaster graph needs a function to go with it

The above rollercoaster graph needs a function to go with it. Select the correct functions that begins at (0,10) and ends at (15,0) with a local minimum at (6,2) and a local maximum at 10,7). You need to select one function for the red piece, one function for the green piece, and one function for the purple piece. e Purple (r) 35+ (s (r-10) f 10 s z s 15 +3.5sin Green (a) 2.5 cos (z -6)) .5 if 6 z 10 Green (a) 2.5 cos (8 (z 6) 4.5 if 6 S z 10 Red (r) 5 5 cos (83) if 0 6 (83) Red (r) 4 6 cos Purple (a) TT (ar 12.5) srs 15 3.5 sin f 10 Purple (r) 3.5 3.5 s f 10 S S 15 ln.

Solution

For Red (x) = 6 + 4*cos(x/6) if 0 x < 6

where at x = 0, Red(x) = 10,

at x = 5, Red(x) = 2.5

For Green (x) = -2.5*cos((x - 6)/4) + 4.5       if    6 x < 10

where at x = 10, Green (x) = 7,

at x = 6, Green (x) = 2.0

For Purple (x) = 3.5 - 3.5*sin((x - 12.5)/5) if 10 x 15

where at x = 10, Purple (x) = 7,

at x = 15, Purple (x) = 0