Lesson Writing a function rule for a function based on its wording description

Writing a function rule for a function based on its wording description

Problem 1

According to the problem, functions g(x) is sinusoidal, has the value of 0 at x= 0 
and has a period  . Hence, g(x) has the form

    g(x) = ,  where real number "b" is the amplitude of g(x).


Function f(x) is sinusoidal, has the value of 0 at x= 0 and has a period, which is 
one-half of that of g(x), i.e. . Hence, f(x) has the form

    f(x) = ,  where real number "a" is the amplitude of f(x).


Next,  we are given   = 4.  It means    = 4,  or   = 4.


Since   = 1,  it gives us  a = 4.


It implies, due to the problem description, that the amplitude of  g(x)  is  2 :  b = 2.


Thus g(x) has the form

     g(x) = .    ANSWER