Use the functions shown :
a. Evaluate each function for x=6 , x=8 and x=12
b. When will function h exceed function f and function g ?

The correct answer is: Function h will exceed functions f & g after point (8,6).

Step-by-step solution:-

a). f(x) = 0.75x
Let x = 6- f(x) = 0.75(6) = 4.5
Let x = 8- f(x) = 0.75(8) = 6
Let x = 12- f(x) = 0.75(12) = 9

∴ We get the points (6,4.5); (8,6) & (12,9) for f(x)
h(x) = 1.25x
                                                                                           Let x = 6- h(x) = 1.25⁶ = 3.81
                                                                                             Let x = 8- h(x) = 1.25⁸ = 6
                                                                                        Let x = 12- h(x) = 1.25¹² = 14.55
∴ We get the points (6,3.81); (8,6) & (12,14.55) for h(x)
g(x) = 0.09375x2
                                                                                       Let x = 6- g(x) = 0.09375(6)² = 3.375
                                                                                          Let x = 8- g(x) = 0.09375(8)² = 6
                                                                                      Let x = 12- g(x) = 0.09375(12)² = 13.5
∴ We get the points (6,3.375); (8,6) & (12,13.5) for g(x)
b). From the above calculations, we observe that the 3 functions have a common point (point of intersection) i.e. (8,6).
Hence, after point (8,6), function h will exceed functions f & g because function h is an exponential function while function f & g are linear and quadratic functions, respectively and we know that the rate of increase for an exponential function is higher than that in linear or quadratic functions.
Final Answer:-
∴ Function h will exceed functions f & g after point (8,6).